[SECTION-I] Direction: This section contains multiple choice questions. Each question has 4 choices (a), (b), (c) and (d), out of which ONLY ONE choice is correct. 1.
2.
Figure shows a system of three masses being pulled with a force F. The masses are F connected to each other by massless strings. The horizontal surface is frictionless. The tension T1 in the first string is 16 N. The acceleration of the system is 1 2 3 (a) (b) (c) m m m
T2
3m
5m
4 m
(d)
(b)
m1 m 2 2
g
(c) m1 m 2 g
m1 m 2 g
(d)
2
A body whose mass is 13 kg appears 12 kg when weighted by mean of a spring balance is in a moving lift. The value of acceleration with magnitude and direction is (a)
4.
T1
Two small balls of same size and masses m1 and m2 (m1 > m2) are tied by a thin weightless thread and dropped from a balloon. The tension T of the thread during the flight after the motion of the balls has become steady will be (a) m1 m 2 g
3.
m
g upwards 12
(b)
g upwards 13
(c)
g downwards 12
Two small blocks of masses m1 and m2 connected by a light inextensible string passing over a smooth pulley are in equilibrium on a fixed smooth wedge. The ratio of the masses m1 and m2 is
g downwards 13
(d)
m1
m2
=60 =30 0
(a) 5.
1 3
(c)
1 3
(d)
1 2
(b) 3 w
(c) 2 w
(d) w
The velocity time graph of a lift moving downwards is a straight line inclined to the time axis at 450. There is small block of mass m kg in the lift. Then the effective weight of block is (in Newton) (take g = 10 ms–2) (a) m
7.
1 2
A parachutist of weight w strikes the ground with his legs fixed and comes to rest with an upward acceleration of magnitude 3g. Force exerted on him by ground during landing is (a) 4 w
6.
(b)
0
(b) 9 m
(c) 10 m
(d) none of these
A body climbs up with a speed v on a smooth inclined plane having inclination 300 and stops at a distance of 17.3m. Now if the angle of inclination be 600, then the distance it will go along the inclined plane with the same speed is (a) 17.3 m
(b) 12.9 m
(c) 10.0 m
(d) 8.6 m
8.
9.
In the figure shown system is released from rest at time t = 0, 2 sec after the start, 4 kg block is stopped and is held stationary. The height to which block 2 kg rises from its position at t = 2s before coming to rest momentarily is (a)
g m 9
(b)
2g m 9
(c)
g m 3
(d)
2g m 3
(a) 2.4 m/s2
(b) 9.4 m/s2
2
2
250 N 15°
(d) 4.9 m/s
In the given figure, all strings and pulleys are ideal and g acceleration of m1 is m/s2 upward. Then find the ratio of 3 m1/m2.
1 3 1 (c) 2 (a)
11.
4kg
A trolley is being pulled up an incline plane by a man sitting on it (as shown in figure). He applies a force of 250 N. If the combined mass of the man and trolley is 100 kg, the acceleration of the trolley will be [sin 15° = 0.26] (c) 6.9 m/s
10.
2kg
(b) 1 (d)
1 4
m1
m2
Consider the situation shown in the figure. acceleration of mass m is (b) g/3 down the plane (a) g/3 up the plane (c) g/2 up the plane (d) g/2 down the plane
The
m 300
12.
13.
In the figure a block of mass M is at rest on the floor. The acceleration with which should a boy of mass m climb along the rope of negligible mass, so as to just lift the block from the floor is M (a) equal to 1g m
M (b) greater than 1g m
M (c) equal to g m
M (d) greater than g m
2m
B a m M
A block of mass m is placed on a smooth inclined plane of inclination with the horizontal. The force exerted by the plane on the block has a magnitude (a) mg tan
(b) mg cos
(c) mg/cos
(d) mg
14.
A block of wood is kept on the floor of a stationary elevator. The elevator begins to descend with an acceleration of 12 ms–2. If g = 10 ms–2, then the displacement of the block during the first 0.2 second after the start is (a) 0.02 m
15.
17.
19.
(d) 0.4 m
(b) 15 dyne
(c) 10 dyne
(d) 5 dyne
In the Atwood machine (data as in figure) P is a massless pulley, and springs S1 and S2 are also massless. If the blocks are set free to move, the readings in S1 and S2 respectively be 1 2 (a) kg; kg 3 3
4 4 (b) kg; kg 3 3
2 4 (c) kg; kg 3 3
2 2 (d) kg; kg 3 3
P S1
S2
1kg 2kg
Two masses m and M are connected by a light string passing over a smooth pulley. When the system set free m moves up by 1.4 m in 2 s. The ratio M/m is (a) 17/3
18.
(c) 0.2 m
A balloon contains 10 g of air. The air begins to escape from a small hole in the balloon at the steady rate of 4 cms–1 and it completely shrinks in 2 seconds. Then the average force on the balloon? (a) 20 dyne
16.
(b) 0.1 m
(b) 15/13
(c) 9/7
(d) 7/9
In the system, the m1 = 300 gm, m2 = 500 gm and F = 1.7N. If the mass and friction of pulley are negligible, then the acceleration of m2 is (a) 9.8 m/s2
(b) 1 m/s2
(c) 1.7 m/s2
(d) 0.88 m/s2
As shown in the figure, two blocks of masses 3 kg and 6 kg are connected by a string of mass 1 kg and placed on a frictionless surface. The system is pulled from the side of block 3 kg with a constant force 20 N. Tension in the string at points A, B and C is (a) 16 N, 14 N, 12 N
(b) 14 N, zero, 12 N
(c) 14 N, 12 N, 10 N
(d) 14 N, 13 N, 12 N
m2
m1
20N
3kg
A
1kg B
F
6kg C
20.
The potential energy of a conservative system is given by U = ay2 – by, where y represents the position of the particle and a as well as b are constants. The force acting on the system will be (a) b 2ay
21.
mMg nm M
500 3
24.
(b)
mMg nmM
(d) ay
n m
4 m
N
3 m
2 m
1 m M
(c) mg
(d) mng
The 50 kg homogeneous smooth sphere rests on the 300 incline A and bears against the smooth vertical wall B. The contact force at B is (g = 10 m/s2) (a) 250 N (b) zero (c)
23.
(c) by
In the given arrangement, n number of equal masses are connected by strings of negligible masses. The tension in the string connected to nth mass is (friction is absent every where) (a)
22.
(b) 2ay b
B
A 300
(d) 500 N
In the given massless and frictionless pulley system, (a) tension in both the strings is zero (b) pulleys B and C rotate counter clockwise and the pulley A clockwise (c) acceleration of A and B are same and is equal to 2g (d) all of the above
B A C m1 m2
Two bodies A and B of masses m1 and m2 respectively are connected by a massless spring of force constant k. A constant force F starts acting on the body A at t = 0. Then (a) at every instant, the acceleration of centre of mass is
k
m2
m1
A
B
F m1 m 2
(b) at t = 0, acceleration of B is zero but that of A is maximum (c) the acceleration of A decreases continuously (d) all of the above 25.
A solid sphere of mass 2 kg is resting inside a cube in the vertical plane as shown in the figure. The cube is moving with a velocity v 5t iˆ 2t jˆ m/s . Here t is the time in second. All surfaces are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube? (take g = 10 m/s2)
(a)
29N
(b) 29 N
y
(c) 26 N
A
B
D
C
O
(d)
89N
x
26.
P
The variation of momentum with time of one of the body in a two body collision is shown in the figure. The instantaneous force is maximum corresponding to point (b) Q (a) P (c) R (d) S
S R Q P
(b)
D
t
(d)
I
(b) 8 m
I
I
(c) 6 m
(d) 30 m v
The velocity-displacement graph (v-x graph) of the motion of particle is shown in the figure. The acceleration-displacement graph (a-x graph) of the motion of the particle is a
(c)
(b) x
v0 x0 x
a
a
(a)
32.
E
A car A is at a distance 10 m from the car B towards north direction. Car A moves towards east with 40 m/s. Car B moves towards north with 30 m/s. The minimum distance between A and B will be (a) 10m
31.
C
A
(c)
I
30.
B
Which of the following graph depicts spring constant k versus length l of the spring correctly? k k k k (a)
29.
x
a
x
(d)
x
x
A ship moves along the equator to the east with a velocity of 30 km/hour. The south eastern wind blows at an angle of 600 to the equator with a velocity of 15 km/hr. The wind velocity relative to the ship (take cos 600 = 0.500 and sin 600 = 0.866) is (a) 35 km /hr nearly
(b) 60 km /hr nearly
(c) 26 km /hr nearly
(d) 50 km /hr nearly
Acceleration of a body moving along a straight line varies with time as shown in the figure. If velocity at t = 7.5 sec is 25 m/sec, velocity at t = 15 sec will be (a) 50 m/s
(b) zero
(c) 35 m/s
(d) 44 m/s
2
28.
Figure shows the displacement of a particle going along the X-axis as a function of time. The force acting on the particle is zero in the region. (a) AB (b) BC (c) CD (d) DE
a(m/s )
27.
t
5 7.510
15
t(s)
33.
The 5 kg cart at rest at t = 0 is acted on by a horizontal force which varies with time as shown. Neglect friction. The velocity of the cart at t = 1 second is (a) 1 m/s (c)
34.
(d)
v sin sin
(c) v cos
(b)
Parabolic
1 m/s 6
2 Time t(s)
A rod length l slides down along an inclined plane and the ground as shown in the figure. At any instant the velocity of end B is v, then the velocity of end A at the same instant will be (a)
35.
Force F(N)
(b) 0.5 m/s
1 m/s 3
20
A u
v cos cos
B
v
(d) v cos
A particle is projected with a velocity v at an angle to the horizontal. At a certain point of its trajectory, its velocity makes an angle
with the horizontal. The radius of curvature of 2
this point is (a)
v2 g cos
36.
2
v 2 cos g cos 2 2
(c)
v 2 cos 3 g cos 2 2
(d)
v 2 cos 2 g cos 3 2
A point moves along an arc of a circle of radius R. Its velocity varies as v a s where a is constant. The angle between the vector of total acceleration and the vector of velocity is given by R (a) tan 1 s
37.
(b)
R (b) tan 1 2s
2s (c) tan 1 R
A body moves according to the equation S
1 t2
s (d) tan 1 R
. Which one of the following
statements is true 5 (a) acceleration is positive and proportional to rd power of velocity 3 3 (b) acceleration is positive and proportional to th power of velocity 5 1 (c) velocity is proportional to rd power of distance 3
(d) velocity and acceleration have the same sign 38.
A particle moves along a circular path of radius r with uniform speed v. The angle described by the particle in one second is given by (a) vr –2
(b) v–2 r
(c) vr –1
(d) v –1r
39.
A boat which has a speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is (a) 1
40.
(b) 3
(c) 4
(d)
41
A rod AB is moving in a vertical plane. At a certain instant when the rod is inclined at 60° to the horizontal, the point A is moving horizontally at 3 m/s, while B is moving in the vertical direction. The velocity of B is
vB B 60°
A (a)
43.
44.
(c)
3 m/s
3 m/s 2
(d)
1 gt 1t 22 2
(b)
t 1 g 12 2 t 2
(c)
1 gt 1t 2 2
(d)
An object is projected up the incline with speed 30 m/s at an angel 300 as shown in the figure. The distance s up the incline at which the object lands is (g = 10 m/s2) (a) 6.0 m
(b) 60 m
(c) 120 m
(d) 600 m
1 2 gt 1 t 2 2
30 m/s
B s
300
300
A car is moving towards east with a speed of 25 km/hr. To the driver of the car, a bus appears to move towards north with a speed of 25 3 km/hr. The actual velocity of the bus is (a) 50 km/hr, 300 east of north
(b) 50
(c) 50 km/hr, 300 west of north
(d) 50 3 km/hr, 300 west of north
3 km/hr, 300 east of north
Second’s hand of a clock is 6 cm long. As shown in the figure, A is a point on the second hand at a distance 3 cm from centre. The change in velocity of A in 15 s will be
(a)
45.
(b) 2 3 m/s
A particle is projected vertically upwards from a point A on the ground. It takes t1 seconds to reach a point B at a height h from A bit still continues to move up. If it takes further t2 seconds from B to ground again, then h is equal to (a)
42.
3
m/s
2 cm/s 10
(b)
2 cm/s 10
(c)
(b) 5 m/s
(c) 2.5 m/s
(d) 7.5 m/s
3cm
O
2 cm/s 30
A body is moving along a straight line. Its speed varies with time as shown in the figure. Average speed of the body for its motion from t = 0 to t = t1 is (a) 10 m/s
A
(d) zero
V(m/s)
41.
1
vA
3 sin1 5 1 10 sin1 2
t1 t(s)
46.
A particle moves along a straight line and at a distance x from a fixed point O on the line, x its velocity is then its acceleration is x
(a) directed towards O and proportional to
1 x
(b) directed towards O and is proportional to
1 x2
(c) directed away from O and is proportional to x (d) directed away from O and is proportional to x2
47.
A ball is thrown upward at an angel 300 to the horizontal and lands on the top edge of a tower that is 20 m away and 5m high. The thrown velocity is (a) 10 m/s
(b) 20 m/s
(c) 40 m/s
(d) 80 m/s
v0
O
48.
5m
300
Displacement-time graph of a body confined to move along a straight line is as shown in the figure. Which of the following graph represents the correct velocity-time variation.
20m
s
t1 t2 t3
(b)
(a) t1 t2 t3 t4 t5
t
t1 t2 t3 t4 t5
v
t
v (d)
(c) t1 t2 t3 t4 t5
t
t1 t2 t3 t4 t5
t
A body starts from rest at t = 0 and moves along a straight line. Its acceleration is given as a t . The body travels a distance of 30m from t = 1 s to t = 2 s. Distance travelled during the fourth second is (approx.) (a) 159 m
50.
t
v
v
49.
t4 t5
(b) 250 m
(c) 350 m
(d) 210 m
Two particle are projected horizontally in opposite directions from the same height at t = 0 with velocities 12 m/s and 3m/s. Relative speed of the two when there velocities become mutually perpendicular is (g = 10 m/s2)
(a) 15 m/s
52.
(d) 9 m/s Velocity (m/sec)
A lift is going up. The variation in the speed of the lift is as given in the graph. What is the height to which the lift takes the passengers (a) 3.6 m (b) 28.8 m (c) 36.0 m (d) Cannot be calculated from the above graph
3.6 0 2 Time (sec) 10 12
Cars X and Y start their journey from the same place with X leaving 3 minutes earlier than Y. The cars move in the same direction with equal accelerations. Time taken after the 1 the distance travelled by X, is departure of X so that the distance travelled by Y 16 (a) 240 sec
53.
(c) 10 m/s
(b) 180 sec
(c) 100 sec 4
Velocity-time (v-t) graph for a moving object is shown in the figure. Total displacement of the object during the time interval when there is non-zero acceleration and retardation is (a) 60 m
(b) 50 m
(c) 30 m
(d) 40 m
(d) 120 sec
3 2
V(m/s)
51.
(b) 12 m/s
1 0 10 20 30 40 50 60 t (sec)
1
55.
56.
(a) (2.5 ± 0.6)g/cm3
(b) (2.5 ± 0.8)g/cm3
(c) (2.5 ± 0.4)g/cm3
(d) (2.5 ± 0.3)g/cm3
(a) 200
(b) 250
(c) 300
(d) 400
15 10 5 0
10 20 30 Time (s)
X
40
An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement (s) – velocity (v) graph of this object is s
s
s
(b)
(a) v
57.
Y
In the following graph, distance travelled by the body in metres is
v(m/s)
54.
3 3 Mass of a spherical object (10±1)g. Its radius is cm with a percentage error of 2%. Density of the object can be expressed as
s
(c) v
The graph of displacement vs time is
(d) v
v
s
t
Its corresponding velocity-time graph will be
v
v
(a)
(c)
(d) Time
Time
Which graph represents the uniform acceleration? s
s
(a)
s
(b)
s
(c)
t
(d)
t
t
t
Which of the following velocity-time graphs shows a realistic situation for a body in motion? v
v
v
(b)
(a)
v
(c)
(d)
t
t
61.
(c) Time
Time
Speed
(b)
Speed
Speed
(a)
60.
t
t
A ball is thrown vertically upwards. Which of the following plots represents the speed-time graph of the ball during its height if the air resistance is ignored
59.
(d)
t
Speed
58.
v
(b)
t
v
t
t
Acceleration-time graph of a body is shown. The corresponding velocity-time graph of the same body is
a
t v
v
(a)
(c)
(d)
t
t
t
An object starts from rest at t = 0 and moves along a straight line. From t = 0 to t = 3 sec, it moves with an acceleration a1 and travels a distance 10m; from t = 3 sec to t = 6 sec, it moves with an acceleration a2 and travels 25m; from t = 6 sec to t = 9 sec; it covers 52 m with acceleration a3. Which of the following is correct. (a) a1 a 2 a3
63.
v
(b) t
62.
v
(b) a1 a 2 a3
(c) a3 a 2 a 3
(d) a 2 a1 a3
The acceleration-time graph of a body is shown below. The most probable velocity-time graph of the body is
a
t v
(a)
(b) t
64.
v
v
v
(c) t
(d) t
t
A shell is fired from a gun with an initial velocity v at an angle with horizontal. At the highest point of trajectory, the shell explodes into two fragments X and Y of equal masses.
Given that the speed of fragment X, immediately after the explosion, is zero, the distance from the gun does the fragment Y strike the ground is (a) 65.
v 2 sin 2 g
(b)
(b) 200
68.
(b)
(b) 20 N, 28 N
(c) 24 N, 20 N
(d) 20 N, 20 N
2v 2 sin 2 g
(d) 100
(c) 1.5 m/s
(d)
98 m/s
4kg
4kg = 0.6
f1
= 0.7
f2
4 kg
A particle is moving in a circle of radius R in such a way that at any instant, the normal and tangential components of its acceleration are equal. If its speed at t = 0 is v0, the time taken to complete the first revolution is R v0
(b)
R 1 e 2 v0
(c)
R 2 e v0
2R v0
(d)
A train is moving with a speed v on a curved railway track of radius r. A spring balance loaded with a block of mass m is suspended from the roof of the train. The reading of the spring balance is mv 2 (b) rg
mv 2 (c) m rg
a
(a)
(b) 4s
t
(b) zero
2
F = 4t
(d)
1m/s2
4s
A block of mass 2 kg start moving with speed 10 m/s at t = 0 on a rough horizontal surface with coefficient of friction 0.2 and a constant force 2 N is also applied opposite to motion of particle at t = 0. Find speed of the particle after 4s. (g = 10 m/s2) (a) 2 m/s
a
(c) 4s
mv 2 rg
4kg
a
1m/s2
t
m
2
(d)
A block of mass 4 kg is kept on a rough horizontal surface with coefficient of friction = 0.4 and a time varying horizontal force F = 4 t applied on it, then the acceleration time graph of the particle is (g = 10 m/s2) a
71.
98 3 m/s
(a) 24 N, 28 N
(a) m 70.
(d)
(c) 150
Three blocks of same mass are connected through string as shown in the figure. The values of f1, f2 are (take g = 10 m/s2 and all strings and pulleys are ideal)
(a)
69.
5 v 2 sin 2 g 2
A motor car has its centre of gravity 1 m above the ground and its wheels are 1.5 m apart. The safe speed at which it negotiates at a level curve of radius 40 m is (a) 9.8 m/s
67.
(c)
A boy whirls a stone in a horizontal circle 2 m above the ground by means of a string 1 m long. The string breaks and the stone flies off horizontally striking the ground 10 m away. The acceleration (in m/s2) during the circular motion is (g = 10 m/s2) (a) 250
66.
3 v 2 sin 2 g 2
t
4s
2kg =0.2
t
10m/s
(c) 4 m/s
(d) 6 m/s
72.
73.
In the arrangement shown in the figure, there is a friction force between the blocks of masses m and 2m. Block of mass 2m is kept on a smooth horizontal plane. The mass of the suspended block is m. Block A is stationary with respect to block of mass 2m. The minimum value of coefficient of friction between m and 2m is (a) 1 /2
(b) 1/ 2
(c) 1 / 4
(d) 1 /3
(b) 1.3 106 N
(c) 1.8 106 N
(d) 1.7 106 N
A block of mass m is released on a smooth inclined surface of wedge of mass M. Find the minimum value of coefficient of friction between wedge and horizontal surface to keep wedge stationary.
(a) 75.
A m B 2m
A 5 million kg ship rests on launching way that slope down to the water at an angle of 100. If the coefficient of sliding friction is 0.2, the force which is required to move down the ship into water is (given g = 10 m/s2, sin 100 = 0.17, cos 100 = 1) (a) 1.5 106 N
74.
mC
m sin 2 2M m
(b)
m sin 2 M m
(c)
m M
m sin 2 2
2 M m cos
Two beads of masses m1 and m2 are connected by a light rigid rod. The system is placed between a rough floor and smooth vertical wall. The coefficient of friction between the rough floor and the bead of mass m2 is . Which of the following is correct?
(d)
m sin 2 2M m cos
m1
N1 T T
smooth
N2 Rough m2
(a) the minimum value of so that the system does not slip is 45° (b) N1 T sin (c) N 2 T sin (d) N 2 N 1 , when the rod is about to slip 76.
Two rods are moving perpendicular to each-other along the axis one on the other with velocities v and 2v, as shown in the figure. The unit vector along which the friction force on the rod moving with velocity v by the rod moving with velocity 2v will act is (a) (c)
1 5 1 5
iˆ 2 ˆj
(b)
3iˆ 2 ˆj
(d)
1 ˆ i 2 ˆj 5 1 5
y jˆ
v
3iˆ 2 ˆj
x iˆ 2v
77.
A block of mass 1 kg is placed on a rough horizontal surface connected by a light string passing over two smooth pulleys as shown. Another block of 1kg is connected to the other end of the string. The acceleration of the system is (coefficient of friction = 0.2) (a) 0.8 g
78.
(c) 0.5 g
1kg (d) zero
The angle of an inclined plane is and the angle of friction is ( > ). The acceleration of a body down the plane is (a)
79.
(b) 0.4 g
1kg
g sin cos
(b)
g sin cos
(c) g sin
Two blocks A and B having equal mass, are placed in contact with each other on a rough plane, inclined at an angle with horizontal as shown in figure. If coefficients of friction for these blocks are 1 and 2 (1> 2) respectively, then for static equilibrium of two blocks
(d) g sin cos
B A
(a) cannot be greater than tan–1 (2) (b) cannot be less than tan–1 (2)
2 (c) maximum possible value of is equal to tan–1 1 2
(d) maximum possible value of is equal to tan–1 80.
1 2
A simple pendulum is suspended from the ceiling of a trolley. As shown, the trolley is moving towards right with a block of mass 2 kg in contact with its vertical side and with such an acceleration that the block is just prevented from falling under gravity. Coefficient of friction between the surfaces of trolley and the block being
a 2kg
1 , inclination of the pendulum to 2
the vertical will be 1 2
(a) sin 1 81.
2 (c) cos 1 5
1 2
(d) tan 1
A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with vertical is (take g = 10 m/s2) (a) zero
82.
2
(b) sin 1 5
(b) 30°
(c) 45°
(d) 60°
A body of mass 10 kg is moving along a circular path of radius 100m. Its speed increases, in a uniform manner, from 17 m/s to 26m/s in a time duration of 3s. Force acting on the body when it is travelling at a speed 20 m/s is (a) 45 newton
(b) 42.5 newton
(c) 47.5 newton
(d) 50 newton
83.
84.
A block of mass m, lying on a rough horizontal plane, is acted upon by a horizontal force P and another force Q, inclined at an angle to vertical. The block will remain in equilibrium, if minimum coefficient of friction between it and surface is
87.
(c) (P + Q cos) / (mg + Q sin )
(d) (P sin – Q) / (mg – Q cos )
A particle of mass m is fixed to one end of a light spring of force constant K and unstretched length l. The system is rotated, about an axis passing through the other end of the spring with an angular velocity , in gravity free space. The increase in length of the spring will be m 2 l K
(b)
m 2 l K m 2
(c)
m 2 l K m 2
K m
(d)
m 12 l K
A body is moving down along inclined plane of slope 370. The coefficient of friction between the body and plane varies as = 0.3x, where x is distance travelled down the plane. The 3 body will have maximum speed ( sin 370 and g 10 m/s2) 5 (b) at x = 2 m
(c) at x = 1.25 m
(d) at x = 2.5 m
A right circular cone is fixed with its axis vertical and vertex down. A particle in contact with its smooth inside surface describes circular motion in a horizontal plane at a height of 20 cm above the vertex. Its velocity in m/s is (a) 1
(b) 1.2
(c) 1.4
(d) 1.6
h=20cm
An automobile car rounds a curve of 80 m radius without slipping, if the road is unbanked and the coefficient of friction between the road and tyres is 0.81. The maximum speed is (a) 12.1 m/s
88.
m
(b) (P cos + Q) / (mg – Q sin )
(a) at x = 1.16 m 86.
P
(a) (P + Q sin) / (mg + Q cos )
(a) 85.
Q
(b) 25.2 m/s
(c) 50.4 m/s
A mass m is hung vertically by means of a thread. It is in contact with vertical surface of a pan as shown. The coefficient of friction between mass m and the pan is . The pan is pulled horizontally with acceleration (a = g) on a smooth horizontal surface. Then the tension in the thread is (a)
T mg 1
(b) T mg 2
(c) T mg
(d) 75.6 m/s Pan a=g m
(d) T 2mg
89.
A block of mass 2 kg is kept on the floor. The coefficient of static friction is 0.4. If a force F of 2.5 N is applied on the block as shown in the figure. The frictional force between the block and the floor will be (a) 2.5 N
90.
(b) 5 N
F
(c) 7.84 N
Two blocks A and B of masses m and M are placed in a platform as shown in the Figure. The friction coefficient between A and B is but there is no friction between B and the platform. The whole arrangement is placed inside an elevator which is coming down with an acceleration f (f < g). What maximum horizontal force F can be applied to A without disturbing the equilibrium of the system? (a) 2mg
(b) 2m(g – f )
(c) 2m(g + f )
(d) 2mf
(d) 10 N
F B
A m
f
M
T
91.
A given object takes n times as much time to slide down a 45° rough incline as it takes to slide down a perfectly smooth 45° incline. The coefficient of kinetic friction between the object and the incline is given by 1 (a) 1 12 (b) 1 2 (c) 1 12 (d) 1 n 2 n 1 n n
92.
On a dry road, the maximum permissible speed of a car along a circular path is 10 m/s. If the road becomes wet, the maximum permissible speed along same path becomes 5 2 m/s. If the coefficient of friction of dry road is , then that for the wet road is
(a) 93.
2
(b)
3
(c)
2 3
(d)
3 4
A block of mass m is placed on a rough horizontal surface. The coefficient of friction between them is . An external horizontal force is applied to the block and its magnitude is gradually increased. The force exerted by the block on the surface is R, then which of the following statement is incorrect. (a) The magnitude of R will gradually decrease. (b) R mg 2 1 . (c) The angle made by R with the vertical will gradually increase. (d) The angle made by R with the vertical tan–1.
94.
In figure two blocks M and m are tied together with an inextensible string. The mass M is placed on a rough horizontal surface with coefficient of friction and the mass m is hanging vertically against a smooth vertical wall. (a) the system will accelerate only when m > M (b) when m < M, T = mg (c) when m > M, Mg < T< mg (d) all of the above are correct
M Rough() m
95.
96.
A block of mass 10 kg is placed in a box as shown in figure. Box is moving with constant acceleration of 5 m/s2 at an angle of 530 from x axis (horizontal direction). Force exerted by box on block in y-direction (vertical direction) will be (g = 10 m/s2, tan 530 = 4/3 ) (a) 140 N
(b) 40 N
(c) 50 N
(d) 150 N
a 0
53 x 10kg
A body of mass m rests on horizontal surface. The coefficient of friction between the body and the surface is . If the mass is pulled by a force P as shown in the figure, the limiting friction between body and surface will be (b) μ mg P 2 3P (d) μ mg 2
(a) mg (c) μ mg P 2 97.
y
P m
30°
A 40 kg slab rests on a frictionless floor as shown in the figure. A 10 kg block rests on the top of the slab. The static coefficient of friction between the block and slab is 0.60 while the kinetic friction is 0.40. The 10 kg block is acted upon by a horizontal force 100 N. If g 9.8 m / s 2 , the resulting acceleration of the slab will be (a) 0.98 m/s2 (b) 147 m/s2 (c) 1.52 m/s2
100 N
10 kg 40 kg
A B
(d) 6.1 m/s2
98.
A uniform chain of mass M and length L is placed such that a part of its lies horizontally on a table and the other part hangs along the vertical as shown in figure. Coefficient of limiting friction being =0.25, what maximum percent of total length could hang vertically without sliding the remaining part? (a) 20% (b) 30% (c) 25% (d) 50%
99.
A 50 kg sphere is projected vertically upwards with a speed of 200 m/s. It rises upto a height of 1500 m. The energy used up in overcoming friction is (take g = 9.8 m/s2) (a) 3.65 104J
100.
(b) 3.75 106J
(c) 4.75 104J
A particle of mass m is released from rest at point A along the inside surface of a smooth hemispherical bowl of radius R. The 2R from the lowest point is speed at B which is at a height h 3 (a)
2gR
(b)
4gR 3
(c)
gR
(d) 2.65 105J A B 2R/3
(d)
2 gR 3
101.
102.
A block of mass m initially at rest dropped from a height h on to a massless spring of force constant k, the maximum compression in the spring is h/4, then spring constant k is mg 40mg (b) (a) h h mg 20mg (c) (d) 2h h
R 4
(d) none of these
(b) 2 sin 3 cos
(c) 3 sin 2 cos
A r
(b) 5.6 m/s
(c) 1.4 m/s
B
(d) 2 sin 3 cos v0 M
(d) 5.8 m/s
(b)
R 3
(c)
R 2
(d) R
(b) heavier one
(c) same for both
(d) cannot be predicated
In hydrogen atom the radius of the orbit of electron changes from r1 to r2 and angular frequency changes from 1 to 2. The ratio of 1 to 2 will be (a) r1/r2
109.
(c) 32 J
Two bodies have same kinetic energy. They are stopped by applying same retarding force. The stopping distance is small for (a) lighter one
108.
(b) 128 J
A small body slides without friction from the top of a hemisphere of radius R. It leaves the hemisphere when it has descended a vertical distance of (a)
107.
(d) 150 J
1 kg block collides with a horizontal weightless spring of force constant 100 N/m, as shown in the figure. The block compresses the spring 0.4 m from the rest position. Assuming that the coefficient of kinetic friction between the block and the horizontal surface is 0.9, the speed of the block at the instant of collision is approximately (g = 10 m/s2) (a) 5 m/s
106.
(c) 240 J
A particle moves from rest at A on the surface of a smooth circular cylinder of radius r as shown. At B it leaves the cylinder. The equation relating and is (a) 3 sin 2 cos
105.
(b) 390 J
If a force F varies with displacement x as F = 3x2 + 4. The work done by force if particle moves from x = 2 to x = 4m is (a) 64 J
104.
h
A ladder 3 m long and weighing 200 N has its centre of gravity 120 cm from the bottom. At its top end is a 50 N weight. The work required to raise the ladder from a horizontal position on the ground to a vertical position is (a) 290 J
103.
m
(b) (r1/r2)2
(c) (r2/r1)2
Two bodies of masses m and 4 m are attached with string as shown in the figure. The body of mass m hanging from a string of length l is executing oscillations of angular amplitude 0, while the other body is at rest.
(d) (r2/r1)3
The minimum coefficient of friction between the mass 4 m and the horizontal surface should be
4m 0
m 2 cos 0 (a) 3
110.
1 cos 0 (c) 2
3 2 cos 0 (d) 4
(b) 5 2 m/s
(c) 10 3 m/s
(d) 20 m/s
A person of mass 60 kg carries a 15 kg body on the top of building 10 m high in 5 minutes. He puts a power in carrying the body (g = 10m/s2) (b) 25 W
(c) 30 W
(d) 15 W
A 50 g bullet moving with a velocity of 10 ms–1 gets embedded into a 950 g stationary body. The loss in kinetic energy of the system will be (a) 100%
113.
10 m, whirling in a 3 circular path in a vertical plane. The ratio of maximum tension in the string to the minimum tension in the string is 4. If g is taken to be 10 m/s2, the speed of the stone at the highest point of the circle is
(a) 10 W 112.
(b) 2 cos 2 0 2
A stone of mass 1 kg tied to a light inextensible string of length L
(a) 10 m/s 111.
l
(b) 95%
(c) 50%
(d) 5%
Potential energy associated with a conservative force is given by U = Ax2 where A is a constant then (a) force always tends to accelerate the particle towards origin (b) force always tends to accelerate the particle away from origin (c) force always tends to accelerate the particle towards the origin if A is positive (d) force always tends to accelerate the particle towards the origin if A is negative
114.
A small block of mass m lying at rest at point P of a wedge having a smooth semi circular track of radius R. What should be the minimum value of horizontal acceleration a0 of wedge so that mass can just reach the point Q? (a) g/2
115.
(b)
(c) g
m P
a0
(d) not possible
A particle hanging by a light string of length l is projected horizontally from its lowest position with a velocity (a) 300
116.
g
Q
7gl . The string slackens after swinging through 2
(b) 450
(c) 1200
(d) 1500
A motor pump is used to deliver water at a certain rate from a given pipe. To obtain n times water from the same pipe in the same time, by what amount the power of motor must be increased? (a) n times
(b) n2 times
(c) n3 times
(d)
n times
117.
If the centre of gravity of an object which is slightly disturbed and the object returns to its original position when the disturbing force is removed, the object is said to be in (a) neutral equilibrium (b) stable equilibrium (c) unstable equilibrium (d) none of these
118.
A force of 0.5 N is applied on upper block as shown in figure. The work done by lower block on upper block for a displacement 3m of the upper block is (take g = 10 m/s2) (a) 1 J
119.
(b) –1 J
= 0.1 F = 0.5N
1kg Smooth
(c) 2 J
2kg
(d) –2 J
An elastic string of unstretched length L and force constant k is stretched by a small x. It is further stretched by another small length y. The work done in the second stretching is (a)
1 2 ky 2
(b)
1 k x2 y 2 2
(c)
1 2 k x y 2
(d)
1 ky 2 x y 2
120.
A body of mass m dropped from a height H reaches the ground with a speed of 1.2 gH . Calculate the work done by air friction. (b) 0.72 mgH (c) – 0.28 mgH (d) – 0.72 mgH (a) 0.28 mgH
121.
The potential energy of particle of mass 0.1 kg moving along the x-axis is given by U 5 x x 4 J , where x is in metre. It can be concluded that (a) the particle is acted upon by a constant force (b) the speed of the particle is maximum at x = 2m (c) the particle cannot execute simple harmonic motion (d) the period of oscillation of the particle is
122.
s 20
ABCDE is a smooth iron track in the vertical plane. The sections ABC and CDE are quarter circles. Points B and D are very close to C. M is a small magnet of mass m. The force of attraction between M and the track is F, which is constant and always normal to the track. M starts from rest at A
A
M
r O
B CD
(b) At B, the normal reaction of the track is F mg (c) At D, the normal reaction of the track is F mg (d) The normal reaction of the track is equal to F at stone point between A and B. Two small balls of masses m and 2m are suspended by light wires of length l, so that they are in contact as shown in figure. Coefficient of restitution between two balls is 1/2. Minimum horizontal velocity that should be imparted to the ball of mass 2m so that ball of mass m can perform a complete revolution is (assuming only one collision take place) (a)
2gl
(b)
7gl
(c)
5gl
r E
(a) If M does not leave the track if F 2mg .
123.
O'
l 2m m (d)
6gl
124.
A body of mass m was slowly pulled by a force which at each point was directed along a tangent to the path. The work done by the applied force
B F
(a) does not depend upon path followed upon path (b) depends upon path
A
(c) does not depend upon positions of A and B (d) both (a) and (c) are correct
127.
(b) 25 J
(c) 300 J
(d) 200 J
A g 2 h1 h22 2hh2 2
20 15 10 5 0 2
A g 2 A g (d) 2
(b)
h
1
4
6
8 x (cm)
(a) 0 m/s
(b) 20 2 m/s
(c) 20 3 m/s
(d) 40 m/s
h2 h22
h1 h h22 2
A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in figure. If it starts its journey from rest at x = 0, its velocity at x = 12 m is
F(N) 10 0
4
12
8
x (m)
A particle is dropped from a height h. A constant horizontal velocity is given to the particle. Taking g to be constant every where, kinetic energy E of the particle w.r.t. time t is correctly shown in E
E
E
(b)
(a) t
130.
5
Two identical cylindrical shape vessels are placed, A at ground and B at height h. Each contains liquid of density and the heights of liquid in A and B are h1 and h2 respectively. The area of either base is A. The total potential energy of liquid of system with respect to ground is
(c) hAg h1 h h2
129.
10
0 5 10 15 20 25 30 35 40 Displacement (m)
A 10 kg mass moves along x-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from x = 0 to x = 8 cm? (b) 16 × 10–2 joules (a) 8 × 10–2 joules –4 (c) 4 × 10 joules (d) 1.6 × 10–3 joules
(a)
128.
Force (N)
(a) 50 J
15
a (cm/sec )
126.
Adjacent figure shows the force-displacement graph of a moving body, the work done in displacing body from x = 0 to x = 35 m is equal to
2
125.
(c) t
The adjoining diagram shows the velocity versus time plot for a particle. The work done by the force on the particle is positive from (a) A to B (c) C to D
(b) B to C (d) D to E
E
(d) t
t
v
B
C D
A
E t
131.
A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F ( x ) kx ax 3 . Here k and a are positive constants. For x 0, the functional from of the potential energy U (x ) of the particle is U(x)
U(x)
U(x)
(a)
(b)
(c)
133.
x
x
x
132.
U(x)
A force F acting on an object varies with distance x as shown here. The force is in Newton and x in metre. The work done by the force in moving the object from x = 0 to x = 6m is (a) 4.5 J (b) 13.5 J (c) 9.0 J (d) 18.0 J
(d) x
F(N) 3 2 1
x (m) 0 1
The potential energy of a system is represented in the first figure. The force acting on the system will be represented by
2
3
4
5
6
7
U(x)
a
x
F(x)
(a)
(b)
a
F(x)
a
x
(c)
F(x)
x
(d)
a
F(x)
x
a
x
134.
A heavy elastic ball X falls freely from a height h on to a smooth horizontal elastic surface. When X strikes the surface, another ball Y is dropped from the same height, they meet after h 2h g h (a) s (b) s (c) s (d) s g 2g 2h g
135.
A 40 kg skater moving at 4 m/s overtakes a 60 kg skater moving at 2 m/s in the same direction and collides with him. Both the skaters move with the same velocity after collision. How much K.E. is lost? (a) 392 J
136.
(b) 48 J
(c) 440 J
(d) 832 J
The kinetic energy of rotation E depends upon the angular momentum J and moment of inertia l . Find the expression for kinetic energy (K is a constant) (a) E
KJ 2 I2
(b) E
KJ 3 I2
(c) E KIJ 2
(d) E
KJ 2 I
137.
138.
Two negatively charged particles having charges e1 and e2 and masses m1 and m2 respectively are projected one after another into a region with equal initial velocity. The electric field E is along the y-axis, while the direction of projection makes an angle with the y-axis. If the ranges of the two particles along xaxis are equal then one can conclude that (a) e1 e2 and m1 m2 (b) e1 e2 only (c) m1 m2 only (d) e1m1 e2m2
2gh 5
(b)
2gh 3
(c)
x
C
m h
2m
gh 3
(b)
mu t
(d)
2gh
(b) 25 cm
u (d) m t g
u (c) m g t
Two blocks of mass 3kg and 6kg are placed on a smooth horizontal surface. They are connected by a light spring of spring constant k = 200 N/m. Initially the spring is unstretched. The indicated velocities are imparted to the blocks. The maximum extension of the spring will be (a) 30 cm
141.
O
A body thrown up vertically with velocity u reaches the highest point in t sec. The mean value of the force of air resistance acting on the body during ascent is (a) mg
140.
E
A mass 2m rests on a horizontal table. It is attached to a light inextensible string which passes over a smooth pulley and carries a mass m at the other end. If the mass m is raised vertically through a distance h and is then dropped, what is the speed with which the mass 2m begins to rise?
(a) 139.
y
2.0m/s
1.0m/s
6kg
3kg
(c) 20 cm
(d) 15 cm
The momentum of a particle is given by P ( 4 sin t iˆ 4 cos t jˆ) kg m/s . Select the correct alternative
(a) Momentum P of the particle is always parallel to F. (b) Momentum P of the particle is always perpendicular to F. (c) Magnitude of momentum P is variable. (d) None of the above. 142.
A particle moves on a rough horizontal ground with some initial velocity say v0. If (3/4)th of its kinetic energy is lost due to friction in time t0 then coefficient of friction between the particle and the ground is (a)
143.
v0 2gt 0
(b)
v0 4gt 0
(c)
3v 0 4gt 0
A block moving with velocity u collides with two identical block placed in the track of first block, after the elastic collision,
v0 gt 0
(d)
m
u
m
m
(a) 1st stops, 2nd and 3rd moves with velocity
u 2
(b) 1st and 2nd stops, 3rd moves with velocity u. (c) 1st returned with velocity
u u , 2nd moves with velocity and 3rd with velocity u. 2 2
(d) None of these 144.
A block of mass m is pushed with a velocity u towards a movable wedge of mass m and height h. All the surfaces are smooth. The minimum value of u for which the block will reach the top of wedge is (b) 2gh (a) 2gh (c)
145.
1 2gh 1
(d)
u
h
m
m
1 2gh1
A block A of mass m moving at a speed v collides with another block B of mass 2 m at rest. The block A comes to rest after collision. The coefficient of restitution is (a)
1 4
(b)
3 4
(c)
1 2
(d) 1
146.
A ball strikes a frictionless horizontal floor at an angle = 450. The coefficient of restitution 1 between the ball and the floor is e . The fraction of its kinetic energy lost in collision is 2 (a) 5/8 (b) 3/8 (c) 3/4 (d) 1/4
147.
A smooth rubber cord of length l with spring constant k is suspended from O. The other end is fitted with a bob B. A small sleeve of mass m starts falling from O. Neglecting the masses of the cord and bob find the maximum elongation of the cord. (a)
(c) 148.
mg k
2kl 1 1 mg
mg k
A
2kl 1 mg
(b)
mg k
(d)
mg 1 k
B
k mg
A force acts on a mass of 40 kg and changes its velocity from 3 m/s to 12 m/s then the impulse of the force is (a) 360 N-s
149.
O
(b) 36 N-s
(c) 600 N-s
(d) none of these
A shell fired along a parabolic path explodes into two fragments of equal mass at the top of the trajectory. One of the fragments returns to the point of firing having retracted its original path. If v is the velocity of projectile at the highest point, then three statements are given as below (i) after explosion, the other fragment moves with 2v along +x-axis (ii) after explosion both fragments reach the ground with separation 2R between them (iii) after explosion, both fragments hit the ground simultaneously at t
R v
150.
(a) only (i) is correct
(b) only (ii) is correct
(c) both (ii) and (iii) are correct
(d) both (i) and (iii) are correct
(a) 20 cm 151.
(b) 10 cm
t
t
(b) 1 m/s
(c) 3 m/s
t 2 m/s
1 m/s
(d) 4 m/s
(b) 1 m/s
(c) 0.1 m/s
(d) 0.01 m/s
A heavy steel ball of mass greater than 1 kg moving with a speed of 2m sec–1 collides head on with a stationary ping-pong ball of mass less than 0.1 gm. The collision is elastic. After the collision the ping-pong ball moves approximately with speed (a) 2 m sec–1
(b) 4 m sec–1
(c) 2 × 104 m sec–1
(d) 2 × 103 m sec–1
A body of mass ‘M’ collides against a wall with a velocity v and retraces its path with the same speed. The change in momentum is (take initial direction of velocity as positive) (a) zero
156.
(d)
(c)
A disc of mass 0.1 kg is kept floating horizontally in mid air by firing bullets of mass 0.05 kg each vertically at it, at the rate of 10 bullets per second. If the bullets rebound with the same speed, what is the speed of the bullets with which these are fired? (g = 10 m/s2) (a) 10 m/s
155.
(d) 15 cm
A ball is moving with velocity 2 m/s towards a heavy wall moving towards the ball with speed 1 m/s as shown. Assuming collision to be elastic find the velocity of ball immediately after the collision (a) 2 m/s
154.
(c) 5 cm
(b) t
153.
A
B
A ball falls from a height on a horizontal surface. If the collision is elastic, the graph between speed (v) and time (t) upto the second collision looks like v v v v
(a)
152.
2 m/s
In the shown diagram m A m B = 1 kg, spring constant = 200 N/m. Initially v B 2 m/s , v A 0 . Find the maximum compression produced in the spring. (Neglect friction)
(b) –2 Mv
(c) Mv
(d) 4 Mv
A gun fires a bullet of mass 50 gm with a velocity of 30 m sec–1. Because of this the gun is pushed back with a velocity of 1 m sec–1. The mass of the gun is (a) 15 kg
(b) 30 kg
(c) 1.5 kg
(d) 20 kg
157.
A metal ball falls from a height of 32 metre on a steel plate. If the coefficient of restitution is 0.5, to what height will the ball rise after second bounce? (a) 2 m (b) 4 m (c) 8 m (d) 16 m
158.
At high altitude, a body explodes at rest into two equal fragments with one fragment receiving horizontal velocity of 10 m/s. Time taken by the two position vectors connecting point of explosion to fragments to make 90° is (a) 10 s (b) 4 s (c) 2 s (d) 1 s
159.
A body of mass m1 moving with a velocity 3 ms 1 collides with another body at rest of mass m2. After collision the velocities of the two bodies are 2 ms–1 and 5 ms–1 respectively along the direction of motion of m1 . The ratio m1 / m 2 is (a) 5 12
(b) 5
(c) 1 5
(d) 12 5
160.
100 g of iron ball having velocity 10 m/s collides with a wall at an angle 30° and rebounds with the same angle. If the period of contact between the ball and wall is 0.1 second, then the force experienced by the ball is (a) 100 N (b) 10 N (c) 0.1 N (d) 1.0 N
161.
An impulse J is applied on a ring of mass m along a line passing through its centre O and parallel to horizontal surface. The ring is placed on a rough horizontal surface. The linear velocity of centre of ring when it starts rolling without slipping is (a) J/m (b) J/2m (c) J/4m
162.
Ball 1 collides with an another identical ball 2 at rest as shown in figure. For what value of coefficient of restitution e, the velocity of second ball becomes two times that of 1 after collision (a) 1/3
163.
(b)
m u M m
(b) 2 v
(c) 1/4
2
(d) 1/6
(c)
2m u M m
(d)
M u M m
(c) v / 2
(d) v
2 (b) Kinetic energy is mv 2
(d) Kinetic energy is
m 2v 2 2 (M m )
A metal ball of mass 2 kg moving with a velocity of 36 km/h has an head on collision with a stationary ball of mass 3 kg. If after the collision, the two balls move together, the loss in kinetic energy due to collision is (a) 40 J
167.
1
A bag (mass M) hangs by a long thread and a bullet (mass m) comes horizontally with velocity v and gets caught in the bag. Then for the combined (bag + bullet) system (a) Momentum is mvM M m mv (M m ) (c) Momentum is M
166.
(d) J/3m
A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northward with the same speed v. The two particles coalesce on collision. The new particle of mass 2m will move in the north-easterly direction with a velocity (a) v/2
165.
O O
A big ball of mass M, moving with velocity u strikes a small ball of mass m, which is at rest. After collision big ball obtains velocity v. Then what is the value of v (e = 1) (a) M m u M m
164.
(b) 1/2
J
(b) 60 J
(c) 100 J
Consider a body, shown in figure, consisting of two identical balls, each of mass M connected by a light rigid rod. If an impulse J = MV is imparted to the body at one of its ends, what would be its angular velocity?
(d) 140 J L M
M J=MV
(a) V/L 168.
(b) 2V/L
(c) V/3L
In the figure shown, the position-time graph of a particle of mass 0.1 Kg is shown. The momentum at t 2 sec is (a) 0.2 kg m sec–1 (c) 0.1 kg m sec–1
(b) – 0.2 kg m sec–1 (d) – 0.4 kg m sec–1
(d) V/4L x (m) 6 4 2
169.
The force-time (F – t) curve of a particle executing linear motion is as shown in the figure. The momentum acquired by the particle in time interval from zero to 8 second will be (shown geometry is semicircular) (a) – 4N-s (b) + 4 N-s (c) 6 N-s (d) Zero
Force (N)
2
+2 4 –2
2
t (sec)
4 6
4
6 8 Time (s)
170.
A bullet emerges from the muzzle of a gun with a velocity of 300 m/sec. The resultant force 410 5 t . Assuming the force on the bullet when it is in the gun barrel is given by F 400 3 becomes zero at the end of the barrel, find the impulse of the force and mass of bullet. (a) 0.6 N-s and 2 gm (b) 1.2 N-s and 5 gm (c) 12 N-s and 5 gm (d) 2.4 N-s and 2 gm
171.
A particle of mass m moving with velocity u makes an elastic one dimensional collision with a stationary particle of mass m. They are in contact for a very short time T. Their force of interaction increases from zero to F0 linearly in time T / 2 , and decreases linearly to zero in further time T / 2 . The magnitude of F0 is (b) 2 mu / T (a) mu / T (c) mu / 2T (d) None of these
172.
it hits the wall is (a) iˆ ˆj
174.
T/2
t
T
(b) iˆ 2 ˆj
1 . The velocity vector of the sphere after 2
(c) iˆ ˆj
The variation of momentum with time of one of the body in a two body collision is shown in figure. The instantaneous force is maximum corresponding to point (b) Q (a) P (c) R (d) none of these
(d) 2iˆ ˆj P R
Q
P t
Two particles of mass m and 2m, moving in opposite directions collide elastically with velocities v and 2v. Their velocities after collision are respectively. (a) 0, 3v
175.
F0
A smooth sphere is moving on a horizontal surface with velocity vector 2iˆ 2 ˆj immediately before it hits a frictonless vertical wall. The wall is parallel to ˆj vector and the coefficient of restitution between the sphere and the wall is e
173.
F
(b) 3v, 0
(c) 2v, 0
Consider the following two statements (A) Linear momentum of the system of particles is zero
(d) v, 2v
(B) Kinetic energy of system of particles is zero (a) A implies B and B implies A (b) A does not imply B and B does not imply A (c) A implies B but B does not imply A (d) B implies A but A does not imply B 176.
Two identical discs are moving with the same kinetic energy. One rolls and the other slides. The ratio of their speed is (a) 1 : 1
177.
178.
(b)
2: 3
(c) 2 : 3
A disc of mass m and radius r rests on an inclined surface and is supported by a rope that is tangent to the disc and parallel to the inclined surface as shown in the figure. The minimum value of coefficient of static friction, in terms of , that will prevent the disc from slipping down the inclined surface is tan 2
(a)
2 tan 5
(b)
(c)
2 tan 3
(d) tan
(d) 1 : 2
r m
A sphere which is rotating about its own axis is gently lowered down on to a smooth inclined surface making on angle with the horizontal. The initial angular velocity of rotation is . The translational velocity when it reaches the horizontal surface is
R
L
179.
10 gL tan 7
(a)
2gL tan
(b)
(c)
2 2 R 2 10gL tan 7
(d) none of these
A ball kept in a closed box moves in the box making collisions with the walls. The box is kept on a smooth surface. The velocity of the centre of mass (a) of the box remains constant (b) of the box plus the ball system remains constant (c) of the ball remains constant (d) of the ball relative to the box remains constant
180.
All the particles of a body are situated at a distance R from the origin. The distance of the centre of mass of the body from the origin is (a) = R
181.
(b) R
(c) > R
(d) R
A spherical shell first rolls and then slips down an inclined plane. The ratio of its acceleration in two cases will be (a) 5/3
(b) 3/5
(c) 15/13
(d) 13/15
182.
Three uniform rods, each of length 2l and mass m are attached (end to end) to form a triangular frame work. The moment of inertia of the frame work about an axis passing through the midpoints of two of its sides is (a)
183.
1 2 ml 4
1 2 ml 2
(c)
3 2 ml 4
(d)
5 2 ml 4
The moment of inertia of a ring about its geometrical axis is I, then its moment of inertia about its diameter will be (a) 2 I
184.
(b)
(b) I/2
(c) I
(d) l/4
A Yo-Yo is placed on a rough horizontal surface and a constant force F pulls it vertically, which is less then its weight. Then
F
(a) it will move towards left C
(b) it will move towards right (c) the friction force acts towards left
O
(d) both (a) and (c) are true 185.
186.
The angular momentum and the moment of the inertia are respectively (a) vector and tensor quantities
(b) scalar and vector quantities
(c) scalar and scalar quantities
(d) vector and vector quantities
The kinetic energy of rotation of particle is 18 joule. If the angular momentum vector coincides with the axis of rotation and the moment of inertia of the particle about this axis is 0.01 kg-m2, then its angular momentum will be (a) 0.06 J-sec
187.
188.
(b) 0. 6 J-sec
(c) 0.006 J-sec
(d) zero
The point with position vector r1 is the centre of mass of a set of particles each of mass m while the point with position vector r2 is the centre of mass of a second set of particles each of mass (m). The position vector r for the centre of mass of the combined set of all the masses will be given by r1 r 2 r1 r 2 r1 r 2 r1 r2 (a) r (b) r (c) r ` (d) r 1 1 2 r1 r 2
A small ring is free to move on a smooth wire bent in the form of a vertical circular loop of radius r. The loop is rotating with constant angular velocity about the vertical diameter while r from the axis. The angular velocity the ring remains at rest relative to wire at a distance 2 of ring is equal to (a)
2g r
(b)
2g r 3
(c)
3g r
(d)
3g 2r
189.
A beam is supported at its centre on a fulcrum and forces acts as shown. The force F for the beam to be in equilibrium is (a) 67 N
(b) 12 N
(c) 46.26 N
(d) 35 N
12N
23N
F
23 mm 80 mm 100 mm
190.
A carpet of mass M made of inextensible material is rolled along its length in the form of a cylinder of radius R and is kept on a rough surface (floor). The carpet starts unrolling without sliding on the floor when a negligibly small push is given to it. The horizontal R is velocity of the axis of cylindrical part of the carpet when its radius reduces to 2 (a)
191.
9gR 2
h a
(d)
1 gR 4
(b) 1.5 R
(c) 2.5 R
(d) 4.5 R
(b) 21 N
(c) 15 N
(d) 0 N
(b)
2a h
(c)
a h
(d)
A particle of mass 2 kg is moving with uniform velocity along the line y
a 2h x
2 in the XY 3 plane. X-component of its velocity is 15 m/sec. Angular momentum (magnitude) of the 1 particle about the point 1m, m is 3
(a) 60 kg m2/sec 195.
2 gR 5
A rectangular block has a square base measuring a a and its height is h. It moves on a horizontal surface in a direction perpendicular to one of the edges. The coefficient of friction is . It will topple if (a)
194.
(c)
A force of 15 N is applied to a spanner at an effective length of 140 mm from the centre of a nut. The magnitude of the force required to produce the same moment if the effective length is reduced to 100 mm is (a) 2.1 N
193.
14gR 3
Two spherical bodies of masses M and 5 M and radii R and 2R respectively are released in free space with their initial separation between their centres equal to 12R. Then the distance covered by the smaller body just before collisions is (a) 7.5 R
192.
(b)
(b) 40 kg m2/sec
(c) zero
(d) 30 3 kg m2/sec
A solid sphere, starting from rest, rolls down (without slipping) an inclined plane of length s and inclination . Its speed when it reaches the bottom of the plane is (a)
2gs sin
(b)
4 gs sin 3
(c)
16 gs sin 9
(d)
10 gs sin 7
196.
A cubical block of side a is moving with velocity v on a horizontal smooth plane as shown in figure. It hits a ridge at point O. The angular speed of the block after it hits O is
a M
v O
(a) 197.
v 4a
(b)
v 2a
(c)
v
(d) zero
2a
If a hollow cylinder and a solid cylinder are allowed to roll down an inclined plane, which will take more time to reach the bottom (a) Hollow cylinder
(b) Solid cylinder
(c) Same for both
(d) One whose density is more
198.
A thin uniform circular ring is rolling down an inclined plane of inclination 30° without slipping. Its linear acceleration along the inclined plane will be (b) g/3 (c) g/4 (d) 2g/3 (a) g/2
199.
A solid cylinder rolls down an inclined plane of inclination 30°, the acceleration of cylinder is 2g g g (a) (b) g (c) (d) 3 2 3
200.
Three particles of masses 1.0 kg, 2.0 kg and 3.0 kg are placed at the three vertices of a right-angled triangle of side 6 cm, 8 cm and 10 cm as shown in the figure. Find the centre of mass of the system in terms of coordinates along the X-axis and the Y-axis.
201.
(a) (2.7 cm, 3 cm)
(b) (3 cm, 3 cm)
(c) (2 cm, 2 cm)
(d) (4 cm, 4 cm)
Y 3.0kg 10.0cm
6.0cm
O 1.0 kg 8.0cm
A disc is rolling (without slipping) on a horizontal surface. C is its center and Q and P are two points equidistant from C. Let v p ,v Q and v C be the
2.0 kg
X
Q C P
magnitude of velocities of points P, Q and C respectively, then (a) v Q v C v P
202.
(b) v Q v C v P
(c) v Q v P , v C
vP 2
(d) v Q v C v P
A circular disc of radius R and thickness R has moment of inertia I about an axis passing 6 through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere. The moment of inertia of the sphere about its diameter as axis of rotation is 2I (b) (c) I (d) I (a) I 8 5 10
203.
One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is (a) 1 MR 2 2
204.
(b) 1 MR 2 4
(c) 1 MR 2 8
90°
(d)
2 MR 2
A particle undergoes uniform circular motion. About which point on the plane of the circle, will the angular momentum of the particle remain conserved (a) Centre of the circle
(b) On the circumference of the circle
(c) Inside the circle any point
205.
(d) Outside the circle any point The torque acts on a body about a given point is found to be equal A L where A is a constant vector and L is the angular momentum of the body about that point. Chose the incorrect option. (a) dL is perpendicular to L at all instants of time dt (b) The component of L in the direction of A does not change with time (c) The magnitude of L does not change with time (d) L does not change with time
206.
A
An equilateral triangle ABC formed from a uniform wire has two small identical beads initially located at A. The triangle is set rotating about the vertical axis AO. Then the beads are released from rest simultaneously and allowed to slide down, one along AB and the other along AC as shown. Neglecting frictional effects, the quantities that are conserved as the beads slide down, are
B
O a
C
(a) Total angular momentum and total energy (b) Angular velocity and moment of inertia about the axis of rotation (c) Total angular momentum and moment of inertia about the axis of rotation (d) None of these 207.
A block P of mass m is placed on a frictionless horizontal surface. Another block Q of same mass is kept on P and connected to the wall with the help of a spring of spring constant k as shown in the figure. s is the coefficient of friction between P and Q. The blocks move together performing SHM of amplitude A. The maximum value of the friction force between P and Q is (a) kA (b) kA (a) Zero 2
Q Smooth Surface
(b) s mg
P
208.
A large open tank has two holes in the wall. One is a square hole of side L at a depth y from the top and the other is a circular hole of radius R at a depth 4y from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both the holes are the same. Then, R is equal to (a)
209.
L 2
(c) L
(d)
L 2
A drop of oil is placed on a glass plate and another glass plate is placed over it. The drop of oil flattens into a film 10–4 m thick. If the coefficient of viscosity of oil is 1.5 Nm–2 s and if the area of the glass plates is 0.1 m2 each, the force required to slide one plate over the other with a steady speed of 2 mm/s, is (a) 1.5 N
210.
(b) 2 L
(b) 10–4 N
(c) 3 N
(d) 0.1 N
A pipe with a constriction is shown in figure. The diameter at point P is 6 10–2 m and that at point Q is 2 10–2 m. At P, velocity of water is 2 m/s and pressure is 180 kPa. The value of pressure at Q is (a) 180 kPa
(b) 90 kPa
(c) 9.8 kPa
Q P
(d) 20 kPa
211.
A water barrel stands on a table of height h. If a small hole is punched in the side of the barrel at its base it is found that the resultant stream of water strikes the ground at a horizontal distance R from the table. The depth of water in the barrel is R2 R2 R2 4R 2 (b) (c) (d) (a) h 2h 4h h
212.
Suppose the gas in the explosion chamber of a rocket ship is kept at density 1 and a pressure p1 and that it exudes from the chamber into empty space through an opening of area a at one end of the rocket, the thrust produced on the rocket ship is (b) p1 a (c) 2 p1 a (d) 2 p1a (a) 2p1 a
213.
Choose the correct statement about the steady and unsteady flow. (a) in a steady flow velocity at a point remains constant in magnitude as well as in direction (b) in an unsteady flow velocity at two points may vary in direction (c) in an unsteady flow, velocity at two points may vary in magnitude (d) all the above
214.
At a given place where the acceleration due to gravity is g, a sphere of lead of density d is gently released in a column of liquid of density . If d > , the acceleration with which the sphere will fall is (a)
215.
g d d
(b)
g d
(c)
gd
(d)
gd d
A steel ring of radius r and cross-sectional area A is fitted onto a wooden disc of radius R (R>r). If the Young’s modulus of steel is Y, then the force with which the steel ring is expanded is R (a) AY r
(b) AY
R r r
Y R r (c) A r
(d)
Yr AR
216.
217.
In a surface tension experiment, in a capillary tube water rises upto 0.1m. If the same experiment is repeated on an artificial satellite which is revolving around the earth water rises in the capillary tube upto height of (a) 0.1 m
(b) 9.8 m
(c) 0.98 m
(d) full length of capillary tube
The radii of two soap bubbles are r1 and r 2 r 2 r1 . They meet to produce a double bubble. The radius of their common interface is (a)
218.
r1r 2 r1 r 2
220.
r1 r 2 r 2 r1
(d) r 2 r1
(b) Mg – V g
h
2R
(c) Mg + R2hg
(d) g (V + R2h) 2L P
Q
O a T
T R
A spherical soap bubble of radius 1 cm is formed inside another bubble of 3 cm radius. The radius of a single soap bubble maintaining the same pressure difference as inside the smaller and outside the larger soap bubble (in cm) is 1 4
(b)
5 4
(c)
3 4
(d)
7 4
If more air is pushed in a soap bubble, the pressure in it (a) decreases
222.
(c)
In the following figure a wire of radius r fixed lightly at P and Q. The young’s modulus of the material of the wire is Y and a << L. If it is pulled into the form PRQ the tension in the wire is Ya 2 Ya 2 r 2 (b) (a) 2L2 L2 Ya 2 r 2 r 2Ya 2 (c) (d) 2L2 L2
(a)
221.
r1 r 2 2
A hemispherical portion of radius R is removed from the bottom of a cylinder of radius R. The volume of the remaining cylinder is V and its mass is M. It is suspended by a string in a liquid of density where it stays vertical. The upper surface of the cylinder is at a depth of h below the liquid surface. The force on the bottom of the cylinder by the liquid is (a) Mg
219.
(b)
(b) increases
(c) remains same
As shown in figure below water squirts horizontally out of two small holes in the cylinder side and the two streams strike the ground at the same point. If the hole Q is at a height h above the ground and the water level stands at height H above the ground, then the height of P above ground level is (a) 2h
(b) H/h
(c) H – h
(d) becomes zero.
P H
Q h
(d) H/2
223.
224.
We have two different liquids A and B whose relative densities are 0.75 and 1.0 respectively. If we dip two solid objects P and Q having relative densities 0.6 and 0.9 in these liquids, then (a) P floats in A and Q sinks in B
(b) P sinks in A and Q floats in B
(c) P floats in B and Q sinks in A
(d) P sinks in A and Q sinks in B
A cube of each side L floats in a liquid density of 3 times the density of cube. The length of cube outside the liquid will be (a)
225.
L 3
(b)
2L 3
(c)
2L 5
(d)
L 5
A rectangular block of plastic material which is 50 mm long by 20mm wide by 300 mm high has its lower face glued to a bench and a force of 200 N is applied to the upper face and in line with it. The upper face moves 15 mm relative to the lower face. Assuming the deformation to be uniform, the shear strain (in %) in the upper face is (a) 1.5 %
(b) 5 %
(c) 2.5 %
(d) 12.5 %
226.
A uniform solid cube of side 10 cm and made of a material of density 0.6 g/cc is floating in water. An additional mass 300 g is placed on top of the cube. The volume of the cube now lies outside water is (a) 400 cc (b) 300 cc (c) 200 cc (d) 100 cc
227.
Water is filled in a vessel upto a height h. If a hole is h below the free surface, made in the vessel at a depth 2 h water rushing out of the hole is found to strike the base level at a horizontal distance 135 cm as shown. Then the volume of water coming out per unit time if there is a h below the free square hole of side 3cm at a depth 3 surface (g = 10 m/s2) is (a) 2700 cc/sec (b) 3000 cc/sec (c) 3100 cc/sec
228.
229.
135cm
(d) 280 cc/sec
The height of a capillary tube (of diameter d) be filled with a liquid so that the total force on the vertical surface of the vessel be equal to the force on the bottom is (a) h = d (b) h = 2d (c) h = 3d (d) h = d/2 A body floats in water such that a fraction f1 of its volume is submerged at 00C, while a fraction f2 of its volume is found to be submerged at 500C. Given that coefficient of volume f expansion of body is Yb and that of water YW, 2 is equal to f1 (a)
230.
h/2
1 50Yb 1 50Yw
(b)
1 50Yb 1 50Yw
(c)
1 50Yw 1 50Yb
(d)
1 50Yw 1 50Yb
When water droplets merge to form a bigger drop (a) energy is liberated (b) energy is absorbed (c) energy is neither liberated nor absorbed (d) energy may either be liberated or absorbed depending on the nature of the liquid.
231.
232.
If is coefficient of linear expansion (with temperature) and is coefficient of superficial (areal) expansion, then (a) = 2
(b) is nearly equal to 2
(c) = 3
(d) = 3
If a section of soap bubble (radius r) through its centre is considered, the force on one half due to surface tension is (a) 2 rT
233.
(b) 0.1 J/m2
(c) 3 10–4 J/m2
(d) 5 10–4 J/m2
The velocity of a small ball of mass M and density d1, when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is d2, the viscous force acting on the ball will be (a)
235.
(d) 2T / r
A rectangular film of a certain liquid is 5 cms long and 3 cms is breadth. If the amount of work done in increasing its size to 6 cm 5 cms is 3 10–4 J, then the value of surface tension of the liquid is (a) 0.4 J/m2
234.
(c) r 2T
(b) 4 rT
Md 1g d2
d (b) Mg 1 2 d1
(c)
M d 1 d 2 g
A tube of uniform cross-section is used to siphon water from a vessel as shown in figure. The speed with which water leaves the tube at B will be (a)
2g h1 h 2
(b)
2g h2 h1
(c)
2gh1
(d)
2gh 2
(d) Md 1d 2
h1 A h2 B
336.
On mixing impurities, the elasticity of a material (a) decreases (b) increases (c) sometimes increase and sometimes decreases (d) remains same
237.
A cylinder is of length l and diameter d. On stretching the cylinder, an increment l in length and decrease d in diameter are caused. The poisson ratio is (a)
238.
l d l d
(b)
l d d l
(c)
l d l d
(d)
l d l d
Two parallel glass plates are dipping perpendicularly in a liquid of density . The separation between the plates is d and the surface tension is T. The angle of contact for glass is . The capillary rise of the liquid between the plates is (a) T cos / d
(b) 2T cos / dg
(c) 2T / gd cos
(d) T cos / gd
239.
240.
A tank is filled with water to a height H. A hole is made in one of the walls at a depth D below the water surface. The distance x from the foot of the wall at which the stream of water coming out of the tank strikes the ground is given by (a) x 2DH D 1 / 2
(b) x 2gD 1/ 2
(c) x 2DH D 1/ 2
(d) none of these
The reading of a pressure metre attached to a closed water pipe is 3.5 × 10 5 N/m2. On opening the valve of the pipe, the reading of pressure metre decreases to 3 × 10 5 N/m2. The speed of water flowing in the pipe will be (a) 5 m/s
241.
F1L2 F2L1 F2 F1
(b)
F2 L1 F1L2 F2 F1
(c)
L1 L2 2
(d)
L1L2
(b) 60 N
(c) 44 N
(d) 56 N
(b) YA t / l
(c) YAt / l
(d) YAt
(b) Mg/2A
(c) 2Mg/A
(d) 4Mg/A
Water is flowing through a horizontal pipe of non-uniform cross section. The speed of water is 30 cm/s at a place where pressure is 10 cm (of water). The speed of water at the other place where the pressure is half of that of the first place is (a) 100.4 cm/s
247.
(d) 200 m
On suspending a weight Mg, the length l of elastic wire and area of cross section A, if the final length becomes double the initial length, then the instantaneous stress acting on the wire is (a) Mg/A
246.
(c) 100 m
A metal rod of length L, area of cross section A, Young’s modulus Y and thermal linear coefficient of expansion is clamped at both of its ends. If it is heated through t0C, the force acting on the rod is (a) YALt
245.
(b) 25 m
A 20 N metal block is suspended by a spring balance. A beaker containing some water is placed on a weighing machine which reads 40 N. The spring balance is now lowered so that the block gets immersed in the water. The spring balance now reads 16 N. The reading of the weighing machine will be (a) 36 N
244.
(d) 7m/s
If a stretching force F1 is applied on a vertical metal wire then its length is L1 and if force F2 is applied on it then its length becomes L2. The real length of wire is (a)
243.
(c) 10 m/s
The bulk modulus of rubber is 9.8 108 N/m2. The depth a rubber ball be taken in a lake so that its volume is decreased by 0.1% can be (a) 1 km
342.
(b) 15 m/s
(b) 101.4 cm/s
(c) 102.4 cm/s
A wooden object floats in water kept in a beaker. The object is near a side of the beaker. Let P1, P2, P3 be the pressures at the three points A, B and C of the bottom as shown in the figure. (a) P1 = P2 = P3
(b) P1 < P2 < P3
(d) 104.3 cm/s
B A B C
(d) P2 = P3 P1
(c) P1 > P2 > P3 248.
Water is flowing through a horizontal pipe of varying cross section. At any two places, the diameter of the tube is 4 cm and 2 cm. If the pressure difference between these two places be equal to 4.5 cm (water), then the rate of the flow of water in the tube is (a) 308 cm3/s
249.
251.
(d) 403 cm3/s
(b) 20 s–1
(c) 80 s–1
(d) 40 s–1
An ice cube is suspended in vacuum in a gravity-free hall. As the ice melts it (a) will retain its cubical shape
(b) will change its shape to spherical
(c) will fall down on the floor of the hall
(d) will fly up.
A galvanometer of resistance 50 is connected to a battery of 3V along with a resistance of 2950 in series. A full scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 20 divisions, the resistance in series should be (a) 4450
252.
(c) 504 cm3/s
The relative velocity between two parallel layers of water is 8 cm/s and the perpendicular distance between them is 0.1 cm. The velocity gradient is (a) 10 s–1
250.
(b) 904 cm3/s
(b) 5050
(c) 5550
(d) 6050
Two sources of emf 6V and internal resistance 3 and 2 are connected to an external resistance R as shown. If potential difference across battery A is zero, then value of R is
A
B
6V,3
6V,2
R
(a) 1 253.
254.
(b) 2
(c) 3
In the circuit shown, rate of heat production in 12 is 3W. Magnitude of potential difference between points A and B is (a) 5 V
(b) 12 V
(c) 18 V
(d) 30 V
(d) 4 6 A
B
16 12
In the following part of the circuit, potential difference between points A and B equals to (a) 30 V
(b) 45 V
(c) –15 V
(d) –45 V
2 10 A
30V
0.5A 20V 5
2A
B
3 1A
255.
A thin rod having length 20 cm is connected in series with a resistance of 200 and potential difference of 30 V is applied across the combination. Potential gradient along the length of the rod is found to be 25V/m. Resistance of the rod equals to (a) 4
(b) 40
(c) 120
(d) 400
256.
257.
In the circuit shown in the figure, ammeter reading is zero. Then E2 is equal to (a) 120 V
(b) 60 V
(c) 30 V
(d) 15 V
10
E2 5
E1 = 120V
20 A
25
R
The equivalent resistance across AB is 5 7 R (b) R (a) 8 8 (c) 1 R (d) 2 R
C
D R
R
R
A
B R
258.
259.
260.
261.
75
In the circuit shown, magnitude of potential difference between A and B will be (a) 37.5 V
(b) 62.5 V
(c) 112.5 V
(d) 162.5 V
(b) 15 V
(c) 19 V
(d) 23 V
25
100 B
200
2A
In the circuit shown in the figure, if point Q is earthed, potential at point P will be (a) 6 V
A
P
15V
12
9 S
21 R
3
30V
A voltmeter having resistance 6000 is connected in parallel to measure the potential difference across 3000 resistance in the circuit shown aside. Reading of the voltmeter will be
2000
(a) 36V
(d) 18 V
(b) 30 V
(c) 24 V
In the circuit shown a side, current through 6 resistances is 0.5A. Emf (E) and internal resistance (r) of the cell can be
3000
60V
2 3 (E,r) 6
(a) E = 12 V, r = 1 (b) E = 6 V, r = 1 (c) E = 9 V, r = 1 262.
(d) E = 6 V, r = 2
The potentiometer wire shown in figure has length 100 cm and resistance 500 . Balanced length for cell having emf 12V is found to be 40 cm. Then R is (a) 4000
(b) 3000
(c) 1500
(d) 1000
Q
EP = 120V
G 12V
R
263.
In the given circuit, ammeter reading is zero. Then the value of resistance R is (a) 90
(b) 120
(c) 180
(d) 270
A E2=24V
60
R
180
E1=60V
264.
In the circuit shown, potential difference between points X and Y, (Vx – Vy) is equal to (a) 17.5 V
(b) 27.25 V
(c) 31.75 V
(d) 33.75 V
17
X 30V
In the circuit shown in the figure, if the reading of the ammeter is the same with both switches opens as with both closed, then the resistance R has value (a) 900
(b) 600
(c) 450
(d) 100
5
15 Y
365.
R 27V
23
18V
100
A
R
50
300 + – 1.5V
266.
In the given circuit terminal voltage across cell A is (a) 10.5 V
(b) 11 V
(c) 9.75 V
(d) 9. 5 V
A(10V,1) 14
13 B(25V,2)
267.
In the figure shown, current through the cell is (a) 0.25 A
(b) 0.5 A
(c) 0.4 A
(d) 0.33 A
1
1 1
(1V,1)
268.
269.
The total current supplied to the circuit by the battery is (a) 1A (b) 2A (c) 4A (d) 6A
The magnitude of i (in ampere) is (a) 0.1 (b) 0.3 (c) 0.6 (d) 0.4
2
6V
6
3
1.5
60 i
15
5 1A
1A 10
270.
271.
AB is a wire of uniform resistance. The galvanometer G shows zero current when the length AC= 20 cm and CB = 80 cm. The resistance R is equal to (b) 8 (a) 2 (c) 20 (d) 40
80
R G A
20V A
As the switch S is closed in the circuit shown in figure, current passed through it is (a) 4.5 A (b) 6.0 A (c) 3.0 A (d) zero
B
C
4 5V B
2 2 S
372.
373.
274.
275.
An ammeter with internal resistance 90 reads 1.85 A when connected in a circuit containing a battery and two resistors 700 and 410 in series. The actual current will be (a) less than 1.85 A
(b) equal to 1.85 A
(c) greater than 1.85 A
(d) nearly zero
The circuit shown is constructed of resistors each of which has a maximum safe power rating of 0.4W. The maximum potential difference that can be applied between a and b without damaging to any of the resistors is
a
(a) 0.4 V
(b) 1 V
b
(c) 26.4 V
(d) 66 V
R1=160
In the balanced wheatstone bridge circuit as shown in the figure, when the key is pressed, what will be the change in the reading of the galvanometer? (a) no change
(b) increased
(c) decreased
(d) zero
In the given circuit it is observed that the current I is independent of the value of the resistance R6. Then the resistance value must satisfy (a) R1R2R5 = R3R4R6 1 1 1 1 (b) R 5 R 6 (R1 R 2 ) (R 3 R 4 ) (c) R1R4 = R2R3 (d) R1R3 = R2R4 = R5R6
R3=1000
R2=1000
R
R G R
R
R5 I
R1
R2
R6
R3 R4
276.
277.
278.
In the network of resistances as shown in figure, the effective resistance between points A and B is (a) 8 R
(b) 5R
(c) (5/3)R
(d) (8/3)R
(c) 20
(d) 22.5
R
R
B
R
R E,r
r l N
X
Y
l/3 0
R
20
In the circuit shown, value of resistance R is (b) 10
R
A
A potentiometer wire of length l and resistance R is shown in figure. N is null point in balance l condition with XN = . The value of 0 is 3 ER ER (b) (a) 3R r 32r R E R 2r E (c) (d) 3 3R
(a) 7.5
R
R R
0.5A 1.5A
30 2.5 R
279.
In order to quadruple the resistance of a uniform wire, a part of its length was uniformly stretched till the final length of the entire wire was 1.5 times the original length, the part of the wire was fraction equal to (a) 1 / 8
280.
281.
(b) 1 / 6
l 0.5 l
(c) 1 / 10
Following figure shows cross-sections through three long conductors of the same length and material, with square cross-section of edge lengths as shown. Conductor B will fit snugly within conductor A and conductor C will fit snugly within conductor B. Relationship between their end to end resistance is
(d) 1 / 4
3a
2a
A
B
C
(a) RA = RB = RC
(b) RA > RB > RC
(c) RA < RB < RC
(d) information is not sufficient
In the following star circuit diagram (figure), the equivalent resistance between the points A and H will be (a) 1.9444 r (c) 0.486 r
(b) 0.972 r (d) 0.243 r
a
A
D
C
r
B
72°
r
r
r
E r
r F r G
J
H r
r
r I
282.
In the adjoining circuit diagram each resistance is of 10 . The current in the arm AD will be (a)
2i 5
(b)
3i 5
(c)
4i 5
(d)
i 5
E B F i
i A C D
283.
In the circuit of adjoining figure the current through 12 resister will be (a) 1 A 2 (c) A 5
284.
285.
286.
287.
1 (b) A 5
5V
(d) 5 A 6
(a) RC = RD
(b) RB > RA
(c) RC > RB
(d) none of these
(b) T1 T2
(c) T1 = T2
(d) T1 < T2
C 12
E
F
B A
i
T1
V
T2
I
I-V characteristic of a copper wire of length L and area of cross-section A is shown in figure. The slope of the curve becomes
I
(a) More if the experiment is performed at higher temperature (b) More if a wire of steel of same dimension is used (c) More if the length of the wire is increased (d) Less if the length of the wire is increased
O
A The electric field in a region is given by E 3 x (Assume the potential at infinity to be zero)
(b)
2A x2
D
C
V
The voltage V and current I graph for a conductor at two different temperatures T1 and T2 are shown in the figure. The relation between T1 and T2 is (a) T1 > T2
5 10 5V
A
Variation of current passing through a conductor as the voltage applied across its ends is shown in the adjoining diagram. If the resistance (R) is determined at the points A, B, C and D, we will find that
(a) 2Ax2 288.
5
(c)
V
ˆ i . The potential in this region is
2x 2 A
Four capacitors and a battery are connected as shown in the figure. If the potential difference across the 7F capacitor is 6V then
(d)
A 2x 2
(a) the emf of the battery is 30 V (b) the charge on the 3 F capacitor is 78 C (c) the potential difference across the 12 F capacitor is 14.4 V (d) the potential difference across 3F capacitor is 10 V 289.
(c)
3.9F
3F
4 0 b 2 b a 4 0 b a b
2
(b) (d)
+Q a b
4 0 a 2 b a 4 0 b a a2
Find the equivalent capacitance between points A and B in the given figure. (Capacitance of each capacitor is C) (a) (c)
291.
7F
What is the equivalent capacitance of the capacitor shown in the figure? (a)
290.
12F
C 4
(b)
C 5
(d) 3C
C 3
(b) 1.2 mJ
(c) 0.6 mJ
(d) 20 mJ
C
C
C
C
C
B
Under steady state energy stored in 6F capacitor shown in the circuit is (a) 3 mJ
C A
3F
6F
8F
2F E=90V
292.
A non-conducting rod of negligible thickness and length l carries a positive charge Q which is uniformly distributed on it. A particle carrying a charge Q0 is kept at a distance l Q0 from one end of the rod. The potential energy of interaction between the rod and the particle is
(a) 293.
2QQ 0 1 4 0 3l
QQ 0 1 4 0 2l
(c)
l
QQ 0 QQ 0 1 1 In 2 (d) In 2 l 4 0 4 0 3l
A 2F capacitor is connected in series with a capacitor having capacitance XF and a cell having emf E = 100 V is connected across the combination. Energy stored in the system under steady state is found to be 5 mJ. Then X equals to (a) 1
294.
(b)
l
(b) 2
(c) 4
Two charged particles A and B are connected by insulating string having length 30 cm and the arrangement is placed on a smooth insulating surface as shown in the figure, charge on A is 2C and tension in the string is 0.2 N then charge on B will be (a) 1 mC
(b) 1.5 mC
(c) 1 C
(d) 6 A
(d) 3 C
B
295.
296.
A point charge q1 = +1 C is placed at the centre of a hollow conducting neutral sphere having radius 10 cm. Another point charge q2 = –3 C is placed at a distance 30 cm from the centre of hollow sphere. Force exerted by the sphere on q1 is (a) 0.1 N towards left
(b) 0.3 N towards left
(c) 0.9 N towards left
(d) 0.3 N towards right
In the given circuit diagram, find the heat generated on closing the switch(S). (a)
3 CV 2 2
(b) CV2
q2
C
C
S
C
V
1 (c) CV 2 2
297.
q1
2
(d) 2CV
Q
Two large parallel plates having equal and opposite charge Q are placed very close to each other and distance between the plates is d. Find the work done by external agent to increase the separation between plates by d (area of plate is A)
–Q
d (a) 298.
(b)
Q 2d 2 A 0
(c)
3Q 2 d 2 A 0
Five conducting plates of area A are arranged as shown in the figure. Distance between them is d. Find the capacitance between A and B. (a)
299.
Q 2d 2 A 0
4 0 A d
(b)
0 A 4d
(c)
(d)
Q 2d A 0
A
3 A 0 2d
(d)
B 4 A 0 5d
A charge Q is uniformly distributed in a spherical volume of radius R. A particle of charge q and mass m is projected with velocity v 0 from the surface of the sphere to its centre. The minimum value of v0 such that it just reaches the center (assume that there is no resistance on the particle except electrostatic force) of the spherical volume is (a)
300.
301.
Qq 2 0 mR
(b)
Qq 0 mR
(c)
2Qq 0 mR
(d)
Qq 4 0 mR
Two concentric conducting hollow spheres of radii R and 2R are carrying charges Q and –2Q respectively. If the charge on inner sphere is doubled, the potential difference between the two spheres will (a) become two times
(b) become four times
(c) be halved
(d) remain same
Two identical thin rings, each of radius R metres, are coaxially placed a distance R metres apart. If Q1 and Q2 are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of the other is
(a) zero (c) 302.
q 2 (Q1 Q2 ) ( 40R )
(d)
q(Q1 Q2 )( 2 1)
( 4 20R ) ( 4 2 0R )
(b) 8 iˆ
(c) 16 iˆ
(d) 8 5 iˆ
In a parallel-plate capacitor of capacitance C, a metal sheet is inserted between the plates, parallel to them. The thickness of the sheet is half of the separation between the plates. The capacitance now becomes (a) 4C
304.
q(Q1 Q2 )( 2 1)
The electric potential V at any point x, y, z (all in metres) in space is given by V = 4x2 volts. The electric field (in V/m) at the point (1 m, 0, 2 m) (a) 8 iˆ
303.
(b)
(b) 2C
(c) C/2
(d) C/4
In the electric field of a point charge +q a certain charge is carried from point A to B, A to C, A to D and A to E all the points are at same distance from +q charge. Then the work done is
A
+q B
(a) least along the path AB
D
C
(b) least along the path AE
E
(c) zero along any of the paths, AB, AC, AD and AE (d) least along the path AC
305.
In the given circuit, find the heat generated if switch S is closed. 3 1 (b) CV 2 (a) CV 2 2 2 1 (c) CV 2 (d) CV 2 3
C C C S
V
306.
(a)
(b)
(c) +
(d) 2 +
with the x-axis, where tan = 307.
C
An electric dipole of moment p is placed at the origin along the x-axis. The electric field at a point P, whose position vector makes an angle with the x-axis, will make an angle with the x-axis.
B
A
P –q
O
+q
x
tan 2
The electric field at the origin is along the positive X-axis. A small circle is drawn with the centre at the origin cutting the axes at points A, B, C and D having coordinates (a, 0), (0, a), (–a, 0), (0, –a) respectively. Out of the points on the periphery of the circle, the potential is minimum at (b) B (c) C (d) D (a) A
308.
309.
(a) Q (E1a + E2b)
(b) Q (E1a ) 2 (E 2 b ) 2
(c) Q (E1 + E2) a 2 b 2
(d) Q E 12 E 22 )
(b) 4 10–6 N
(c) 6 10–6 N
(d) 8 10–6 N
A thin, metallic spherical shell contains a charge Q on it. A point charge q is placed at the centre of the shell, another charge q1 is placed out side as shown. All three charges are positive. The net electric force on the charge at the centre is (a) towards left
311.
a2 b2
The electric potential V (in volt) varies with x (in metre) according to the relation V 5 4 x 2 . The force experienced by a negative charge of 2 10–6 C located at x = 0.5 m is (a) 2 10–6 N
310.
Charge Q is given a displacement r aiˆ bˆj in an electric field E E1iˆ E 2 ˆj . The work done is
(b) towards right
Q
(c) upward
(d) zero
Three charges Q, + q and +q are placed at the vertices of a right angled triangle (isosceles triangle) as shown in the figure. The net electrostatic energy of the configuration is zero if Q is equal to (a)
q
1 2 (c) – 2q
(b)
q1
q
Q
a
2q
2 2 (d) +q
+q
+q a
313.
Point charge q moves form point P to point S along the path PQRS (figure shown) in a uniform electric field E pointing co-parallel to the positive direction of the Xaxis. The coordinates of the points P, Q, R and S are (a, b, 0), (2a, 0, 0), (a, – b, 0) and (0, 0, 0) respectively. The work done by the field in the above process is given by the expression (a) qEa
(b) –qEa
(c) qEa 2
(d) qE [( 2a ) 2 b 2 ]
The variation of potential with distance R from a fixed point is as shown below. The electric field at R = 5 m is (a) 2.5 volt / m (b) – 2.5 volt / m (c) 2/5 volt / m (d) – 2/5 volt / m
E P S
Q R
Potential in volts
312.
5 4 3 2 1 1 2 3 4 5 6 Distance R in metres
X
314.
The figure gives the electric potential V as a function of distance through five regions on x-axis. Which of the following is true for the electric field E in these regions
V
(a) E1 > E2 > E3 > E4 > E5 (b) E1 = E3 = E5 and E2 < E4 1 2
(c) E2 = E4 = E5 and E1 < E3
3
4
5 x
(d) E1 < E2 < E3 < E4 < E5 315.
In a uniformly charged hollow spherical shell potential (V) changes with respect to distance (r) from centre V
V
V
(b)
(a)
(c) r
r
The electric field due to a uniformly charged sphere of radius R as a function of the distance from its centre is represented graphically by E
E
E
(b)
(a) R
317.
(d)
r
r
316.
V
E
(c)
r
R
(d)
r
O
r
R
What physical quantities may X and Y represent? (Y represents the first mentioned quantity)
Y
(a) Pressure v/s temperature of a given gas (constant volume) (b) Kinetic energy v/s velocity of a particle (c) Capacitance v/s charge at a given constant potential (d) Potential v/s capacitance at a given constant charge 318.
X
A proton is projected with kinetic energy k, against uniform constant electric field and comes to momentary rest after travelling a distance S0. If an particle is projected with same kinetic energy against same electric field, will come to momentary rest after travelling through (a) S0
319.
r
R
(b)
5S0
(c)
S0 2
Figure (a) shows two capacitors connected in series and joined to a battery. The graph in figure (b) shows the variation in potential as one moves from left to right on the branch containing the capacitors, if (a) C1 > C2 (b) C1 = C2 (c) C1 < C2
(d)
S0 2 2 Y
C1
(a)
C2
X (b)
(d) The information is not sufficient to decide the relation between C1 and C2
320.
Two small identical balls P and Q, each of mass 3 / 10 gram, carry identical charges and are suspended by threads of equal lengths. At equilibrium, they position themselves as shown in the figure. What is the charge on each ball.
Thread 600
1 (Given 9 109 Nm2C–2 and take g = 10 ms–2) 4 0
(a) 10–3C
322.
20V
30V
30°
O
10
20
30
X (cm)
6
V (10 V) 5
(b) 5
Q
6
5
Q
5
Q
6
V (10 V) 5
V (10 V) 2.5
(c)
(d) 5
Q
Moon has no atmosphere, because: (a) there is no vegetation on it (c) it is not a planet
(b) it is far away from the earth (d) the escape velocity on it is small.
The ratio of gravitational mass and inertial mass is (a) 2 : 1 (b) 1 : 1 (c) 1 : 2
(d) 3 : 1
The value of acceleration due to gravity at height h from earth surface will half its value on the surface if (R = radius of earth) (a) h
326.
10V
Y
A condenser of 2F capacitance is charged steadily from 0 to 5 Coulomb. Which of the following graphs correctly represents the variation of potential difference across its plates with respect to the charge on the condenser
(a)
325.
(d) 10–4 C
Equipotential surfaces are shown in figure. Then the electric field strength will be (a) 100 Vm–1 along X-axis (b) 100 Vm–1 along Y-axis (c) 200 Vm–1 at an angle 120° with X-axis (d) 50 Vm–1 at an angle 120º with X-axis
6
324.
Q
30cm
(c) 10–7 C
V (10 V) 2.5
323.
P
(cm)
321.
(b) 10–5 C
600
2 1R
(b) h = 2R
(c) h
2 1R
(d) h = R
A satellite of mass m is revolving at height h from earth’s surface. Its orbital velocity will be (a)
gR e2 Re h
(b)
gR e
(c)
gR e Re h
(d)
gR e Re h
327.
Three particles are initially in position 1. They are free to move and come to position 2 after some time. Let U1 and U2 be the gravitational potential energies in position 1 and 2 respectively (neglecting frictional forces). Then (a) U1 U 2
328.
(b) U1 U 2
(c) U1 U 2
(d) none of these
The earth revolves round the Sun in one year. If the distance between them becomes double, the new period of revolution will be (a) 1/ 2 year
(b) 2 2 years
(c) 4 years
(d) 8 years
329.
Two small bodies initially both at rest and to move from a distance of 1m from each other are subject to only their gravitational force of attraction. They approach each other and collide and do not separate. In respect of this collision which of the following statement is true? (a) the total gravitational P.E. of the two masses has increased during collision (b) the total gravitational P.E. of the two masses has decreased during collision (c) the law of conservation of energy holds good. (d) the force of gravitational attraction vanishes when the bodies come in contact.
330.
For a satellite orbiting in circular path around earth kinetic, potential and total energies are K, V and E respectively. Which of the following relation is not true (a) E = – K
331.
(c) U = 2E
(d) K = –2E
The gravitational field in a region is given by E ( 2iˆ 3 ˆj ) N/kg . No work is done by the gravitational field when a particle is moved on the line 3 y kx 5 . The value of k should be
(a) 1 332.
(b) U = –2 K
(b) 2
(c) 3
(d) 4
Two solid spheres each of mass M and radius R is released from rest from large distance apart. Due to mutual gravitational attraction they accelerate towards each other and collide. Velocity of each sphere at the moment they collide equals to (a)
GM R
(b)
2GM R
(c)
GM 2R
(d) M
G 2R
333.
Imagine that earth is rotating at such an angular speed that a body becomes weightless at the equator. If weight of the same body at north pole is 100 kg wt, its weight at a place of latitude 600 will be (a) 75 kg wt (b) 100 kg wt (c) zero (d) 67.5 kg wt
334.
The height of the point vertically above the earth’s surface at which the acceleration due to gravity becomes 1% of its value at the surface is (R is the radius of the earth) (b) 9 R (c) 10 R (d) 20 R (a) 8 R
335.
A planet is moving in an elliptical path around the sun as shown in figure. Speed of planet in positions P and Q are v1 and v2 respectively with SP = r1 and SQ = r2 then v1/v2 is equal to r (a) 1 r2
336.
r (b) 2 r1
v2 S r2
r1
P v1
(c) constant
A bomb blasts on the moon. Its sound will be heard on earth after (a) sound will never be heard (b) 138 minutes (c) 10 minutes (d) 3.7 minutes
r (d) 1 r2
2
Q
337.
The escape velocity for a planet is ve. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be (a) ve
338.
(c)
2
ve 2
(d) zero
(b) 1 : 8
(d) 1 : 73/2
(c) 1 : 49
At what angle with the horizontal should a projectile be fired with the escape velocity to enable it escape from gravitational pull of the earth? (a) Less than 45°
340.
ve
The distances of two satellites from the surface of the earth are R and 7R. Their time periods of rotation are in the ratio (a) 1 : 7
339.
(b)
(b) More than 45°
(c) Equal to 45°
A homogeneous bar of length L and mass M is at a distance h from a point mass m as shown. The force on m is F.
(d) Any angle
m
M h
GMm (a) F (h L ) 2
341.
343.
h2
GMm (c) F h(h L )
L (d) F
GMm L2
A particle is projected vertically upwards from the surface of earth (radius Re) with a kinetic energy equal to half of the minimum value needed for it to escape. The height to which it rises above the surface of earth is (a) Re
342.
(b) F
GMm
(b) 2Re
(c) 3Re
(d) 4Re
If the radius of the earth were to shrink by 1% its mass remaining the same, the acceleration due to gravity on the earth’s surface would (a) Decrease by 2%
(b) Remain unchanged
(c) increase by 2%
(d) Increase by 1%
The radius and mass of earth are increased by 0.5%. Which of the following statements is not true at the surface of the earth (a) g will increase
(b) g will decrease
(c) Escape velocity will remain unchanged (d) Potential energy will remain unchanged. 344.
To determine time, an astronaut in earth satellite should use (a) either a spring watch or a pendulum clock (b) a spring watch (c) neither a spring watch nor a pendulum clock (d) a pendulum clock
345.
A body of mass m is taken from earth surface to the height h equal to radius of earth, the increase in potential energy will be 1 1 (b) mgR (c) 2 mgR (d) mgR (a) mgR 2 4
346.
An artificial satellite moving in a circular orbit around the earth has a total (kinetic + potential) energy E 0 . Its potential energy is (a) E 0 (b) 1.5E 0 (c) 2E 0 (d) E 0
347.
A tunnel is dug along one of the diameters of the earth. The force on a particle of mass m distant x from the centre in this tunnel will be
348.
GM e mR 3 GM e mx GM e mx (c) (d) 2 2 x R x R R3 The radius of the earth is increased by a factor of 5. By what factor its density be changed to keep g same? 1 1 1 (a) (b) (c) (d) 5 25 5 5
(a)
349.
GM e m
(b)
A uniform sphere of mass M and radius R exerts a force F on a small mass m situated at a distance of 2R from the centre O of the sphere. A spherical portion of diameter R is cut from the sphere as shown in figure. The force of attraction between the remaining part of the sphere and the mass m will be (a)
7F 9
(b)
2F 3
(c)
R
m
R
O
2R
4F 9
(d)
F 3
350.
A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius (1.01)R. The period of the second satellite is larger than that of the first one by approximately (a) 0.5% (b) 1.0% (c) 1.5% (d) 3.0%
351.
If the distance between the earth and the sun becomes half its present value, the number of days in a year would have been (a) 64.5 (b) 129 (c) 182.5 (d) 730
352.
Assuming the earth to have a constant density, point out which of the following curves show the variation of acceleration due to gravity with distance from the centre of earth. g
g
(b)
(a) R
353.
(c)
r
R
(d) none of these
r
R
r
The diagram showing the variation of gravitational potential of earth with distance from the centre of earth is V
(a) O
V
(b) O
R r
354.
g
V
(c) O
R r
V
(d) O
R
R
r
A sphere of mass M and radius R2 has a concentric cavity of radius R1 as shown in figure. The force F exerted by the sphere on a particle of mass m located at a distance r from the centre of sphere varies as (0 r )
r
R1 r
R2
F
F
(a)
F
(b)
(c)
r
355.
r
r
I
(a)
r
I
(b)
I
(c)
r
r=a
r=a
(d)
r
r=a
r
r
r=a
Which of the following graphs represents the motion of a planet moving about the sun? 2 (a) T
2 (b) T
R
357.
(d)
Which one of the following graphs represents correctly the variation of the gravitational field (I) with the distance (r) from the centre of a spherical shell of mass M and radius a I
356.
F
2 (c) T
3
R
3
2 (d) T
R
3
R
Figure shows a long straight wire carrying a current of I. A particle of charge q0 (positive) is moving parallel to the wire at a distance of r. The speed of the particle is v. The force (magnitude and direction)on charge by current in wire are 0 q 0 vI , radially towards the wire 2r q vI (c) 0 0 , away from the wire 4 r
(a)
(b)
I
3
v r
q0
0 q 0 vI , radially towards the wire 2r
(d) zero
358.
The magnetic susceptibility of a material of a rod is 499. Permeability of vaccum is 4 × 10–7 henry/m. Absolute permeability of the material of the rod in henry per meter is (a) × 10–4 (b) 2 × 10–4 (c) 3 × 10–4 (d) 4 × 10–4
359.
A non-planar loop of conducting wire carrying a current I is placed as shown in the figure. Each of the straight sections of the loop is of length 2a. The magnetic field due to this loop at the point P (a, 0, a)points in the direction 1 1 (b) (a) jˆ kˆ ˆj kˆ iˆ 2 3 1 ˆ ˆ 1 ˆ ˆ ˆ (c) (d) i j k i k 3 2
360.
Two long wires are hanging freely. They are joined first in parallel and then in series and then are connected with a battery. In both cases, which type of force acts between the two wires? (a) attraction force when in parallel and repulsion force when in series (b) repulsion force when in parallel and attraction force when in series (c) repulsion force in both cases (d) attraction force in both cases
z y
x
I 2a
Wire 1 Wire 2
Wire 1 Wire 2