PHYSICS Daily Practice Problems Target IIT JEE 2011 Class : XI (PQRS)
Marks : 58
Date : 09-10/09/2009 09-10/09/20 09
Time : 60 min.
DPP. DPP. NO.-52
Q.1 Q. 1
Block of mass m is lowered lowered from natural natural length position position of spring slowly by an external exter nal agent to equilibrium equilibrium position position.. The extensi extension on presen presentt in the mass mass less less sprin spring g was asked from two students students [3] 1 kx2 = mg x Student A : 2 2mg k \ x= k Student B : mg = kx m mg \ x= k (A) Student-A Student- A is incorrect, Student-B Student- B is correct. corr ect. (B) Student-A Student-A is correct, Student-B Student-B is incorrect. incorrect. (C) Both are correct (D) Both are incorrect incorrect
Q.2 Q. 2
A man is standing st anding on incline incline which makes q with horizontal and rain is falling vertically with respect to man. Now man starts walking along the incline. Mark the correct option opt ion.. [3] [3] (A) If man walks up the incline, rain may appear to come horizontally q (B) If man walks down the incline, rain may appear to come horizontally (C) No matter whether man walks walks up or down, rain can never never appear to come c ome horizontally horizontally.. (D) If man walks (up or down) along incline rain may appear to come along the incline.
Q.3
A block slides down on the track tr ack shown below. Comment on its speed and acceleration in the direction of motion ? (friction is absent everywhere) [3] Speed Acceleration (A) decreases decreases (B) decreases increases increases (C) increases increases decreases (D) increases increases
Q.4 Q. 4
A ball is thrown vertically upward under the influ influence ence of gravity. gravity. Suppose observer A films films this motion motion and play the tape backwards (so the tape begins with the ball at its heighest point and ends with it reaching the point from which itit was released), and another observer B observes obser ves the motion of the b ball all from a frame of reference moving at constant c onstant velocity which which is equal to the t he initial initial velocity of the ball ball.. The ball ball has has a downwa downward rd accelerati acceleration on according according to observer observer.. [3] [3] (A) (A) and (B) (B) only (A) (C) only (B) (D) neither neither
Q.5 Q. 5
You are are pushing pushing a wooden crate across the floor floor at a constant constant speed. You decide decide to change change the orientation of crate crat e such that area of contact with floor become half. half. In the new new orientation, to push the same crate across the t he same floor floor with the same constant speed, the force that you apply must be about ________ as the force required before you changed the crate’s orientation. [3] [3] (A) 4 times as great (B) 2 times as great (C) equally equally great (D) 1/2 as great
Q.6 Q. 6
A Coast Guard ship ship is traveli tra veling ng at a constant velocity of 12.50 m/s, m/s, due west , relative to the water. On his radar screen the navigator detects an object that is moving at a constant velocity. The object is located at a distance of 2500 m with with respect to the t he ship, ship, in a direction 53° south of east. One minute minute later, he notes that the object’s position relative to the ship has changed to 1250 m, 37° west of north. What are the magnitude and direction of the velocity of the object relative to the water? Express the [3] [3] direction as an angle angle with respect to t o west. (A) 50 2 m/s at 45°
Q.7
(B) 50 m/s at 30°
(C) 50 3 m/s at 60° (D) None of these
The moon does not fall fall to Earth because : (A) The net force on it is zero. zero . (B) It is beyond beyond the pull of Earths Eart hs gravity. gravity. (C) It is being pulled by the sun and planets as well as by Earth. (D) The statement is wrong : moon is in a state of free fall.
[3] [3]
Page-1
Paragraph for question nos. 8 to 10 Newton’s Cradle is an apparatus consisting identical elastic steel balls carefully aligned along a horizontal line, just touching. The ball on one end is pulled aside and projected towards next ball, as a result of which, the one ball on the far end is knocked away from the others with the same speed as the first ball had initially and all of the other balls remain nearly at rest. If you pull back two balls and let them strike the others, two balls are knocked from the other end, and all the other balls remain nearly at rest. Why does this happen?
This is generally explained by saying that this is the only outcome that conserves both energy and momentum. [Not so. There are many others.] 1
2
3
Consider three balls. Balls 2 and 3 are stationary. Ball 1 hits ball 2 with speed V. Ball 3 moves away with speed V leaving balls 1 and 2 stationary. Momentum and energy are both conserved. Why are other results impossible? Let us consider three balls of equal mass of 1kg each. The first is projected with a speed of 6 m/s towards other two. Let's consider 2 separate models which give different values of v even satisfying basic laws of physics. Model-1, the observed outcome Quantity
Initial
Initial
Initial
Final
Final
Final
Ball-1
Ball-2
Ball-3
Ball-1
Ball-2
Ball-3
velocity
6
0
0
0
0
6
momentum
6
0
0
0
0
6
kinetic energy
18
0
0
0
0
18
Model-2, Two balls emerge at the same speed. Quantity
Initial
Initial
Initial
Final
Final
Final
Ball-1
Ball-2
Ball-3
Ball-1
Ball-2
Ball-3
velocity
6
0
0
-2
4
4
momentum
6
0
0
-2
4
4
kinetic energy
18
0
0
2
8
8
Observation of the experiment shows us the one energy and momentum-conserving outcome that actually happens: Ball 1 comes to rest and ball 3 moves away with speed V. This tells us that moving ball 1 experienced forces that brought it to rest. It tell us that ball 2, initially at rest, ends up at rest. From this we conclude that ball 2 experienced equal size and oppositely directed impulses due to compressional forces at its two faces.
Q.8
Q.9
The fact that ball 2 has zero net displacement tells us that the work done on it by compression forces is zero. Finally, these compressions at the two interfaces did work of equal size and opposite sign on balls 1 and 3. What is the defect in model-2 : [3] (A) The law of conservation of momentum is not obeyed (B) The law of conservation of energy is not obeyed (C) Neither law of conservation of momentum nor conservation of energy is obeyed (D) It does not predict actual results of experiment In the given situation, : [3] (A) All the forces acting to the left did positive work on the ball concerned and all the forces acting to the right did negative work on the ball concerned. (B) all the forces acting to the right as well as left concerned did negative work on the ball concerned (C) all the forces acting to the left or to the right did positive work on the ball concerned (D) all the forces acting to the left did negative work and forces acting to the right did positive work on Page-2 the ball concerned.
Q.10
2 elastic balls of same mass hit an identical ball. The observed outcome is that left most ball comes to rest and 2 balls move on with same speed. Which of the statement is correct : [3] (A) this is the only way conservation laws are obeyed (B) the net impulse on the middle ball is zero (C) the net work done on left most ball is zero (D) the net impulse on right most ball is zero
Q.11
Statement-1 : If the centre of mass of a system is at the origin then the total mass to the right of origin is same as total mass to left of origin. [3] Smi xi
Statement-2 : xcm = Sm i (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for statement-1 (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True
Q.12
Statement-1 :A man starts walking towards west. Friction force on him acts towards east. Statement-2 : Friction opposes relative motion [3] (A) Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for statement-1 (B) Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True
Q.13
Consider a particle at rest which may decay into two (daughter) particles or into three (daughter) particles. Which of the following is true in the two - body case but false in the three-body case ? [4] (There are no external forces and the masses of daughter particles are known.) (A) Velocity vectors of the daughter particles must lie in a single plane. (B) Given the total kinetic energy of the system it is possible to determine the speed of each daughter particle. (C) Given the speed(s) of all but one daughter particle, It is possible to determine the speed of the remaining particle. (D) The total momentum of the daughter particles is zero.
Q.14
Two blocks of masses m1 and m2 are placed in contact with each other on a horizontal platform. The coefficient of friction between the platform and the two blocks is the same. The platform moves with an acceleration. The force of m1 m2 a [4] interaction between the blocks is (A) zero if m1> m2 (B) zero if m1< m2 (C) nonzero if both are sliding relative to the platform (D) zero if both are sliding relative to platform
Q.15
A single conservative force acts on a 1 kg particle that moves along x-axis. The potential energy of the particle varies with x as U = 20 + (x – 2) 2 , here U is in joules and x is in meters. When the particle is at x = 5 m, its kinetic energy is 20 J. Then which of the following is/are correct ? [4] (A) Mechanical energy of particle is 49 J. (B) Least and greatest value of x between which particle can move is (2 – 29 ) m and (2 + 29 ) m respectively. (C) Maximum kinetic energy of the particle is 29 J. (D) At x = 2, the body is in equilibrium.
Q.16
In Column-I, 4 situations are depicted and in column-II, 4 possible kinds of collision are listed. [5] Match the situation with type of collision. Column-I Column-II Before After (A) (B) (C)
Q.17
3m/s
1.5m/s
1.8m/s
2kg
8kg
2kg
8kg
2m/s
1m/s
1m/s
2m/s
2kg
8kg
2kg
8kg
3m/s
1m/s
2kg
8kg
3.4m/s 2kg
1.8m/s
(P)
Elastic
(Q)
Perfectly Inelastic
(R)
Partially elastic
0.6m/s 8kg
(S) Collision is not possible At a time when mining asteroids has become feasible, astronauts have connected a line between their 600 kg space ship and a 1200 kg asteroid. Using their ship’s engine, they pull on the asteroid with a constant force of 450 N. Initially the space ship and the asteroid are at rest, 225 m apart. How much time (in second) does it take for the ship and the asteroid to meet? (Neglect gravitational interaction). [5] Page-3
PHYSICS Daily Practice Problems Target IIT JEE 2011 Class : XI (PQRS)
Q.1
Date : 11-12/09/2009
Time : 60 min.
A 44-kg chandelier is suspended 1.5 m below a ceiling by three wires, each of which has the same tension and the same length of 2.0 m (see the drawing). Find the tension in each wire. [3] (A)
Q.2
Marks : 59
550 N 3
(B)
1760 N 9
(C)
440 3
N
DPP. NO.-53 1.5m
2.0m
(D) 220 N
The person in the drawing is standing on crutches. Assume that the force exerted on each crutch by the ground is directed along the crutch. If the coefficient of static friction between a crutch and the ground is 0.90, determine the largest angle qMAX that the crutch can have just before it begins to slip on the floor. (A) tan –1 (0.9) (C) sin –1 (0.9)
[3] r
–1
(B) cot (0.9) (D) cos –1 (0.9)
F
q
Q.3
An astronaut floating weightlessly in space shakes a large iron block rapidly back and forth. She compares that to her moving it on earth on a smooth horizontal surface. She find that [3] (A) the shaking costs her no effort because there is no weight of block. (B) the shaking costs her some effort but considerably less than on Earth. (C) although weightless, the effort required is same (D) the shaking costs her more effort than on earth. y
Q.4
Consider the setup of a Ferris wheel in an amusement park. The wheel is turning in a counterclockwise manner. Contrary to the illustration, not all seats are aligned horizontally, i.e. parallel to the x-axis. Determine the orientation of the normal to the seat as it passes the point A. [3] (A) parallel to the x-axis (B) in the first/third quadrants (C) parallel to the y-axis (D) in the second/fourth quadrants.
Q.5
x
w
A
The following set of figures show two cases of collision between two balls. Let u1 and u 2 be the r
r
r
velocities before collision and V1 , V2 be the velocities after collision.
r
[3]
u
1
A
d
u
u
2
B
A
1
u
2
B
The coefficient of restitution, V2 - V1 r
e=
r
u1 - u 2 r
r
Student-A : Equation holds for both cases as e is property of material of the colliding bodies. Student-B : Equation holds for case II only. (A) Student-A is incorrect, Student-B is correct. (B) Student-A is correct, Student-B is incorrect. (C) Both are correct (D) Both are incorrect Page-4
Q.6
A wire is bent into the structure as shown in the figure, and placed on a table. It consists of two half rings of radius R and two straight parts of length pR. The height of COM from the table is. [3] (A)
2R
(B)
p
R
p
(C)
R
p R
R
(D) zero
2
Paragraph for question nos. 7 to 9 An elevator car has a mass of 1400 kg and is carrying passengers having a combined mass of 200 kg. A constant friction force of 4000 N opposes its motion.
The elevator cable can withstand a maximum tension of 28000 N. It is being driven by a motor fixed at the top. Q.7
How much power must the motor deliver to lift the elevator car and its passengers at a constant speed of 3 m/s. [3] 4 4 4 4 (A) 6 × 10 W (B) 4.8 × 10 W (C) 1.2 × 10 W (D) 3.6 × 10 W
Q.8
The elevator is moving upwards. What can not be a possible acceleration of the elevator. (A) 5 m/s2 (B) 10 m/s2 ¯ (C) 14 m/s2 ¯ (D) 8 m/s2 ¯
[3]
Q.9
Consider a time when elevator is moving up and retarding : (A) The power supplied by the motor must be negative (B) The power supplied by the motor must be positive (C) The power supplied by the motor must be zero (D) The power supplied by the motor may be positive.
[3]
Paragraph for question nos. 10 to 12 Ram is preparing for IIT JEE. He set s on to tackle a typical problem in mechanics. He sees that the wedge is kept on a smooth ground and it’s inclined surface is also smooth. A block is projected on it as shown. Both the block and wedge have equal mass. Can you help him find the answer to following three questions ?
Q.10
v 0 m
m
q
He sets on to find the maximum height attained by the block, assuming the block does not fall off to [3] the other side. Which of the following equations is correct. (A) mgh =
1 2
mv 20 (by conservation of energy) where h is maximum height of the block.
(B) 02 = v 20 –2gsinq × s where s is maximum displacement along the inclined surface (C) mv0 = mv + mv (by conservation of momentum) and
1 2
mv 02 =
1 2
mv 2 +
1 2
mv 2 + mgh
(D) None of these Page-5
Q.11
How does the path of block look like as seen from ground.
(A)
Q.12
(B)
[3]
(C)
(D)
What is the radius of curvature of it’s path at the highest point ? (A) 0
(B)
v 02 cos 2 q g(sin q cos q + sin 2 q)
(C)
v 20 cos 2 q 2g (1 + sin 2 q)
[3]
(D) None of these
Q.13
Two persons standing on a frictionless surface throw a ball back and forth. Which statement(s) is true ? (A) The interaction mediated by the ball is repulsive. [3] (B) If we film the action and play the movie backward, the interaction appears attractive. (C) The total momentum of the two persons and ball is conserved. (D) The total mechanical energy of the two people is conserved.
Q.14
A particle of mass m kg is displaced from one given point to another given point under the action of several conservative and non-conservative forces (Neglect relativistic considerations). Now match [5] the following. Column -I Column-II (A) Displacement of particle (P) Path dependent (B) Work done by conservative force (Q) Path independent (C) Work done by non-conservative force (R) Frame dependent (D) Angular displacement (S) Frame independent (T) Dependent on location of observer in a given frame
Q.15
The drawing shows a baggage carousel at an airport. Your suitcase has not slid all the way down the slope and is going around at a constant æ 625 ö cm ÷ as the carousel turns. The coefspeed on a circle of radius ç è 8 ø ficient of static friction between the suitcase and the carousel is 0.8, and the angle q in the drawing is 37°. How much time (in second) is required for your suitcase to go around once? (Assume limiting friction) (Take p2 = g) [5]
Q.16
Q.17
The drawing shows a skateboarder moving at 7.0 m/s along a horizontal section of a track that is slanted upward by 45° above the horizontal at its end, which is 0.45 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height H (in m)to which she rises above the end of the [5] track.
q
H 7m/s 0.45m
A cannon of mass 10 × 10 3 kg is rigidly bolted to the earth so it can recoil only by a negligible amount. The cannon fires a 2.1 × 10 3 kg shell horizontally with an initial velocity of 550 m/s. Suppose the cannon is then unbolted from the earth, and no external force hinders its recoil. What would be the velocity (in m/s)of a shell fired horizontally by this loose cannon? (Hint: In both cases assume that the burning [5] gunpowder imparts the same kinetic energy to the system.) Page-6
