PG Brainstormer - 2H
PG Brain Stormer - 2 H RECTILINEAR MOTION, PROJECTILE MOTION/2D MOTION, MOTION, RELATIVE MOTION
An Ultimate Tool to understand advanced High School Physics
T im e A llo w e d
ASHISH H ARORA Sir by ASHIS
9 0 M in
M a x im um M a r k s
11 0
Instruction : In Section A each question is of 3 Marks and there there is a negative marking marking of -1 Mark whereas in Section B there is no no negative marking and each question question is of 5 Marks
Section - A Single Choice Correct (Q. No. 1 to 20)
Y X A L A G S C I S Y H P
The Questions given in this section are MCQs with four answer options (A), (B), (C) and (D) out of which ONLY ONE is correct. Choose the correct answer and fill the answer answer in the OMR sheet provided at the end. –1
1.
A boy moves on a cycle with a velocity of 4 km h . The rain appears to fall on him with a velocity of 3 km h –1 vertically. vertically. The actual velocity of of the rain is : –1 (A) 7 km h (B*) 5 km h –1 (C) 4/3 km h –1 (D) 3/4 km h –1
2.
ˆ ) metre at time t = ˆ ) ms –1. A particle has position vector ( 3iˆ jˆ 2 k = 0. It moves with constant velocity ( iˆ jˆ 3k The position vector (in m) of the particle after 3 second is is : ˆ ˆ ˆ (A*) 2 jˆ 7k (B) 2iˆ k (C) jˆ (D) 3 k
3.
Car A and car B move on a straight straigh t road and their velocity versus time graphs are ar e as shown in figure. Comparing Compari ng the motion of car A in between t = = 0 to t = = 8 sec. and motion of car B in between t = = 0 to t = = 7 sec, pick up the th e correct statement : v (m/s)
v (m/s)
10m/s
10m/s
t = = 2s
t = = 8s
Car A
t (s) (s)
t = = 3s
t = = 7s
t (s) (s)
Car B
1. Distance travelled by car A is less than distan ce travelled by car B. 2. Distance travelled by car A is greater than dista nce travelled by car B. 3. Average Average speed of both cars ar e equal. 4. Average Average speed sp eed of car A is less than average speed of car B. (A) 1 and and 3 ar are corr rreect (B*) 1 and 4 are corr rreect (C) 2 and 3 are correct
(D) 2 and 4 are correc rect
4.
Rain is falling vertically downwards with a speed of 4 km –1 . A girl moves on a straight road with a velocity of 3 km h –1 . The apparent apparen t velocity of of rain with respect r espect to the girl is : –1 –1 (A) 3 km h (B) 4 km h (C*) 5 km h –1 (D) 7 km h –1
5.
An armoured car 2 m long and an d 3 m wide is moving at 10 ms –1 when a bullet hits it in a direction making an angle 3 tan –1 4 with the length of the car as seen by a stationar y observer. observer. The bullet enters one edge of the car at the corner and passes pa sses out at the diagonally opposite corner. Neglecting any interaction between the car an d the bullet, the time for the bullet to cross the car is : (A*) 0.20 s (B) 0.15 s (C) 0.10 s (D) 0.50 s
6.
To a man walking at the rate of 4 km h –1 , the rain appears to fall vertically. If the apparent velocity of rain is 4 3 km h –1, then inclination in clination of the real velocity of of the rain with th e vertical will be : (A) 60º (B*) 30º (C) 45º (D) 90º
PG Brainstormer - 2H 7.
A hunter tries to hunt a monkey with a small, very poisonous arrow, blown from a pipe with initial speed v0. The monkey is hanging on a branch of a tree at height H above the ground. The hunter is at a distance L from the bottom of the tree. The monkey sees the arrow leaving the blow pipe and immediately loses the grip on the tree, falling freely done with zero initial velocity. The minimum initial speed v0 of the arrow for hunter to succeed while monkey is in air : (A*)
8.
g(H
2
L2 )
2 H
2
(B)
2
gH
(C)
H 2 L2
2
g(H L ) H
(D)
2 gH 2 H
2
L2
A man travelling in car with a maximum constant speed of 20 m/s watches the friend start off at a distance 100 m ahead on a motor cycle with constant acceleration 'a'. The maximum value of 'a' for which the man in the car can reach his friend is : v a (A*) 2 m/s2 (B) 1 m/s2 100 (C) 4 m/s2 (D) None of these
Y X A L A G S C I S Y H P
9.
A river is flowing from west to east at a speed of 5 units. A man on the south bank of the river, capable of swimming at 10 units in still water, wants to swim across the river in shortest time. He should swim in a direction : (A*) due north (B) 30º east of north (C) 30º west of north (D) 60º east of north
10.
Rain, pouring down at an angle with the vertical has a speed of 10 ms –1. A girl runs against the rain with a speed of 8 ms –1 and sees that the rain makes an angle with the vertical, then relation between and is : 8 10 sin 8 10 sin (A) tan = (B*) tan = (C) tan = tan (D) tan = cot 10 cos 10 cos
11.
Ship A is travelling with a velocity of 5 km h –1 due east. A second ship is heading 30º east of north. What should be the speed of second ship if it is to remain always due north with respect to the first ship ? (A*) 10 km h –1 (B) 9 km h –1 (C) 8 km h –1 (D) 7 km h –1
12.
A stationary person A throws a ball as shown with speed 20 m/sec at an angle of 45° with horizontal. At the same instant, another person B, at a distance of 10 m from A starts running with constant velocity and catches the ball at point C . The velocity of ball and velocity of person B always lie in same vertical plane; also the vertical level of point of projection and point of catching the ball from ground is same. Then the speed v of person B will be (g = 10 m/s2, Neglect air friction) u
B
A
V
C
10m
(A) 15 2 m/sec 13.
14.
(B*) 7.5 2 m/sec
(C) 6 2 m/sec
(D) 2.5 2 m/sec
A man swims from a point A on one bank of a river of width 100 m. When he swims perpendicular to the water current, he reaches the other bank 50 m downstream. The angle to the bank at which h e should swim, to reach the B directly opposite point B on the other bank is : (A) 10º upstream (B) 20º upstream 1 00 m (C) 30º upstream (D*) 60º upstream A
An airplane pilot wants to fly from city A to city B, which is 1000 km due north of city A. The speed of plane in still air is 500 km hr –1 . The pilot neglects the effect of the wind and directs his plane due north and 2 hours later find himself 300 km north-east of city B. The wind velocity is : (A*) 150 km hr –1 at 45º north of east direction (B) 106 km hr –1 at 45º north of east direction –1 –1 (C) 150 km hr at 45º north of west direction (D) 106 km hr at 45º north of west direction
15.
16.
17.
18.
PG Brainstormer - 2H A river flowing from west to east at a speed of 5 m per min ute. A man on the south ban k of the river, capable of swimming at 10 m per minute in still water wants to swim across the river to a point directly opposite in the shortest time. He should then swim in a dir ection : (A) 60º west of north (B) 30º east of north (C*) 30º west of north (D) 60º east of n orth An airplane flies from a town A to a tow B when there is n0 wind and takes a total time T 0 for a return trip. When there is a wind blowing in a direction from town A to town B, The plan's time for a similar return trip, T w, would satisfy : (A*) T 0 < T w (B) T 0 > T w (C) T 0 = T w (D) The result depends on the wind velocity between the towns.
Y X A L A G S C I S Y H P
A particle is projected at point A from an inclined plane with inclination angle as shown in figure. The magnitude of projection velocity is u and its direction is perpendicular to the plane. After some time it passes from point B which is in the same horizontal level of A, with velocity v . Then the angle between u and v will be : (A) (B) 2 (C*) – 2 (D) 90 +
A projectile is thrown at an angle with the horizontal on an inclined plane of inclination = 30° as shown in figure. If the projectile strikes the inclined plane horizontally then : (Neglect air friction) (A*) tan =
2 3
(B) tan = 2 3
(C) tan = 3
(D) tan = 3 3
u
A
u
B
Ground
n e p l a d e l i n I n c
Horizontal surface
19.
A man holding a flag is running in North-East direction with speed 10 2 m/s. Wind is blowing in east direction with speed 20 m/s. Then the direction in which flag will flutter is : (A) West (B) South (C) South-west (D*) South-east
20.
Two trucks are moving on para llel tracks. A person on one truck projects a ball vertically upward the n path of the ball as seen by four observers from the ground, from the second truck moving with same velocity as that first truck, from the second truck moving with speed greater than first one in same direction and from the second truck moving with speed less than th e first truck in same direction are : (A) Parabola, Parabola, Parabola and Parabola (B) Straight line, Straight line, Parabola and Parabola (C*) Parabola, Straight line, Parabola and Parabola (D) None of these
Section - B More than one Choice Correct (Q. No. 21 to 30)
The Questions given in this section are MCQs with four answer options (A), (B), ( C) and (D) out of which ONE or MORE than ONE answers may be correct. Choose all the correct answer options and fill the answer in the OMR sheet provided at the end. You will get marks in a question only if all the answer options of that question are chosen by you. 21.
An aeroplane flies along a straight line from A to B with a speed v0 and back again with the same speed v0. A steady wind v is blowing. If AB = l then : 2v l (A*) Total time for the trip is 2 0 2 , if wind blows along the line AB v0
(B*) Total time for the trip is
v 2l
v02
v2
, if wind blows perpendicular to the line AB
(C) Total time for the trip decreases because of the presence of wind (D*) Total time for the trip increases because of the presence of wind
22.
23.
24.
PG Brainstormer - 2H A cat starts moving rectilinearly (initial velocity zero) first with an acceleration of 5 ms then uniformly and finally decelerating at the same rate till it stops. Total time of journey is 25 s and average velocity during the journey is 72 kmh –1. Then : (A*) Total distance travelled by the car is 500 m (B*) Maximum speed attained during the journey is 25 ms –1 (C*) Car travels with uniform speed for 15 s (D*) Car acceleration for 5 s and decelerates also for 5 s –2
At the instant a motor bike starts from rest in a given direction, a car overtakes the motor bike, both moving in the same direction. The speed time graphs for motor bike and car are represented by OAB and CD respectively. Then : (A*) At t = 18 s the motor bike and car are 180 m apart (B) At t = 18 s the motor bike and car are 720 m apart (C*) The relative distance between motor bike and car first decreases then increases (D) The relative distance between motor bike and car always remains same
A
60 ) s / m C n 40 i ( d e e p
Y X A L A G S C I S Y H P
B
C
20
O
3
6
9 12 15 18 21 24 27
A particle having a velocity v = v0 at t = 0 is decelerated at the rate | a | = v , where is a positive constant : 2 v0 (A*) The particle comes to rest at t = (B) The particle will come to rest at infinity
(C) The distance travelled by the particle is
2v03/ 2
3/ 2 2 v0 (D*) The distance travelled by the particle is 3
25.
Two particles P and Q moves in a straight line AB towards each other. P starts from A with velocity u1 and an acceleration a1. Q starts from B with velocity u2 and acceleration a2. They pass each other at the midpoint of AB and arrive at the other ends of AB with equal velocities : 2(u 2 u1 ) (A*) They meet at midpoint at time t = (a1 a2 ) 4(u 2 u1 ) ( a1u 2 a 2u1 ) (B*) The length of path specified i.e. AB is l = ( a1 a 2 ) 2 (C*) They reach the other ends of AB with equal velocities if (u2 + u1) (a1 – a2) = 8 ( a1u2 – a2u1) (D) They reach the other ends of AB with equal velocities if (u2 – u1) (a1 + a2) = 8 (a2u1 – a1u2)
26.
A man throws a stone vertically up with a speed of 20 ms –1 from top of a high rise building. Two seconds later, an identical stone is thrown vertically downward with the same speed 20 ms –1. Then : (A*) The relative velocity between the two stones remains constant till one hits the ground (B*) Both will have the same kinetic energy, when they hit the ground (C*) The relative acceleration between the two is equal to zero, till one hits the ground (D*) The time interval between their hitting the ground is 2 seconds
27.
Mark the correct statement(s) : (A*) If speed of a body is varying, its velocity must be varying and it must have non-zero acceleration (B) If velocity of a body is varying, its speed must be varying (C*) A body, moving with varying velocity, may have constant speed (D) A body moving with varying speed may have constant velocity if its direction of motion remain s constant
28.
The velocity of a particle is zero at t = 0 : (A*) The acceleration at t = 0 may be zero (B*) If acceleration is zero from t = 0 to t = 10 s, the speed is also zero in this interval (C*) If speed is zero from t = 0 to t = 10 s, the acceleration is also zero in this interval (D*) If acceleration is zero from t = 0 to t = 10 s, the displacement is also zero in this interval
29.
A projectile is thrown with a speed of 100 m/s making an angle of 53º with the horizontal at time t = 0. The magnitude of angle between its velocity and the horizontal (in direction of initial horizontal component of velocity) will be 45° at instant of time t = : (Take sin37° = 3/5)
(A*) 2 sec 30.
(B) 6 sec
(C) 12 sec
PG Brainstormer - 2H (D*) 14 sec
A standing man, observes rain falling with velocity of 20 m/s at an angle of 37º with the vertical. The man then moves with constant horizontal velocity and observes the rain to fall at an angle 45° with the vertical. Then th e speed of man can be : (A*) 4 m/s (B*) 10 m/s (C*) 14 m/s (D) 32 m/s
*
*
*
*
*
Y X A L A G S C I S Y H P
PG Brainstormer - 2H
PG Brain Stormer - 2 H RECTILINEAR MOTION, PROJECTILE MOTION/2D MOTION, RELATIVE MOTION
An Ultimate Tool to understand advanced High School Physics
Time Allow ed
by ASHISH ARORA Sir
90 M in
M ax imum M arks
11 0
OMR Sheet for the PG Brainstormer - 2H
Y X A L A G S C I S Y H P A
B
C
D
A
1
16
2
17
3
18
4
19
5
20
6
21
7
22
8
23
9
24
10
25
11
26
12
27
13
28
14
29
15
30
B
C
D
PG Brainstormer - 2H
PG Brain Stormer - 2 H RECTILINEAR MOTION, PROJECTILE MOTION/2D MOTION, RELATIVE MOTION
An Ultimate Tool to understand advanced High School Physics
Time Allow ed
by ASHISH ARORA Sir
90 M in
M ax imum M arks
11 0
A N S W E R K E Y
Section - A 1. 10. 19.
(B) (B) (D)
2.
(A) (A) (C)
3.
(B) (B)
4.
(C) (D)
5.
(A) (A)
6.
(B) (C)
7.
(A) (A)
25.
(A) (B) (C)
8.
(A) (C)
Y X A L A G S C I S Y H P 11. 20.
12.
13.
14.
15.
16.
17.
18.
(A) (A)
27.
(A) (C)
9.
Section - B
21. 28.
(A) (B) (D) (All)
22. 29.
(All) (A) (D)
23. 30.
(A) (C) (A) (B) (C)
24.
(A) (D)
26.
(All)
