DPP_Impulse & Momentum

1. At time t = 0, a bullet is fired vertically upwards with a speed of 100 ms–1. A second bullet is fired vertically upwards from the same point and with the same speed at t = 5s. Then, (a) The two bullets will be at the same height above the ground at t = 12.5 s

(b) The two bullets will reach back their starting point at t = 25s (c) The two bullets will have the same speed at t = 20 s

(d) The maximum height attained by either bullet will be 980 m.

2. A pearl of mass m is in a position to slide over a smooth wire. At the initial instant the pearl is in the middle of the wire. The wire moves linearly in a horizontal plane with an acceleration a in a direction having angle  with the wire. The acceleration of the pearl with respect to wire is

a 

(a) gsinacos (b) gsingcos

(c) gsinacos (d) gcosasin 3. Two bodies have undergone an elastic one–dimensional

collision along x–axis. Figure shows six lines corresponding to position versus time curve of both bodies and their centre of mass before and after the collision. The line segments corresponding to the motion of center of mass before and after the collision are

(a) CP and PF (b) BP and PE (c) AP and PD (d) BP and PF

4. A particle is projected with a certain velocity at certain angle with the horizontal surface. The range of the particle is observed to be R. If co-efficient of restitution between the particle and surface is e, then the range of the particle after one collision will be (neglect friction)

(a) R (b) eR (c) e2R (d) R/e

5. A ball A moving with kinetic energy E, makes a head on elastic collision with a stationary ball with mass n times that of A. The maximum potential energy due to deformation stored in the system during the collision is

(a) nE/(n+1) (b) (n+1)E/n (c) (n–1)E/n (d) E/n

6. Inclined surface of a smooth wedge of mass 6 kg makes an angle of 60° with horizontal as shown. A ball hits the wedge horizontally and elastically with a velocity of 40 m/s and moves vertically with respect to ground after the collision. Find the mass (in kg) of the ball if the wedge can also move on the smooth floor.

elastically with rough ground at an angle  with vertical as shown. What can be the minimum coefficient of friction between the particle and the ground if the particle rebounds vertically after collision? (Given tan  = 2)



8. An insect sits on the end of a long board of length 5 m. The board rests on a frictionless horizontal table. The insect wants to jump to the opposite end of the board. What is the minimum take-off speed (in m/s) of insect relative to ground, that allows the insect to do the trick? The board and the insect have equal masses. (g = 10 m/s2)

1. The velocity-displacement graph of a particle is given in figure. The line PR is normal to the curve at point P. The acceleration of the particle at point P is (a) 2 m/s2 (b) 4 m/s2 (c) 6 m/s2 (d) 1 m/s2 (4, 0) (6, 0) P v s R

2. A mass m is hung vertically with the help of a thread. It is in contact with vertical surface of a block as shown. The coefficient of friction between mass m and the block is 0.5. The block is pulled horizontally with acceleration (a = g) on a smooth horizontal surface. The tension in the thread is

(a) 1.5mg (b) 2.5mg

(c) mg (d) 2mg

m

a=g

3. Three masses are connected with a spring and a string as shown. They are initially at rest, with spring at its natural length and string just taut without tension. The maximum extension in the spring, after the forces start acting as shown, will be

(a) F/K (b) 2F/K (c) F/2K (d) 4F/K

4. 2n identical cubical blocks are kept in a straight line on a horizotnal smooth surface. The distance between the consecutive blocks is same. The blocks 1, 3, 5, …, (2n – 1) are given velocity v to the right whereas blocks 2, 4, 6, …, 2n are given velocity to the left. All collisions between blocks are perfect elastic. The total number of collisions that will take place is 1 2 3 4 5 2n–1 2n (a) n (b) n + 1 (c) 2 ) 1 (n n (d) n(n1)

5. A smooth sphere of mass m strikes a second sphere of mass 2m which is at rest. After the collision their direcitons of motion are at right angles. Then coefficient of restitutions is

(a) 0 (b) 2 1 (c) 2 1  (d) 1

Farther from the wall is a more massive block B of mass M ( > 1), initially at rest. The block A undergoes elastic collision with the block B and the wall. If two blocks undergoes only collision then maximum value of  is

A v0 B

(a) 1 (b) 2

(c) 3 (d) 4

7. A pendulum bob is raised to a height 0.2 m and then released. At the bottom of its swing, it picks up an identical bob. To what height (in cm) will the combined mass rise? (Take g = 10m/s2)

8. A small sphere of mass m = 1 kg is moving with a velocity (4iˆ ˆj) m/s. It hits a fixed smooth wall and rebound with velocity (iˆ3ˆj)m/s. The coefficient of restitution between the sphere and the wall is

16 n

. Find value of n.

9. The ends of a chain lie in piles at A and C. When given an initial speed 10 m/s, the chain keeps moving freely at that speed over the fixed pulley B. Neglecting friction, determine the required value of h (in m). (Take g = 10 m/s2)

1. A block (mass m) is resting on the top of a smooth wedge (mass M) resting on a smooth surface as shown in figure. Now system is set free to move. When block gets separated from the wedge, the velocity of block is v1, towards left and velocity of wedge is v2 towards right. The work done by normal (exerted by the wedge on the block) on the block is

m M h (a) ₁2 2 1 mv (b) ₁2 2 1 mv  (c) 22 2 1 Mv (d) 22 2 1 Mv 

2. Two identical balls of mass M and radius R are placed in contact with each other on a frictionless horizontal surface as shown. The third ball of mass M and radius

2 R

moves vertically downward and hits the two balls symmetrically with speed v0 and comes to rest. The speed of two bigger balls after collision will be

(a) 5 4v₀ (b) 5 2v₀ (c) 5 0 v (d) none of these

3. In the above problem, if the smaller ball does not stop after collision, but continues to move downwards with a speed of

2

0 v

after the collision, then the speed of each bigger ball after collision will be (a) 5 4v₀ (b) 5 2v₀ (c) 5 2 0 v (d) none of these

4. A force exerts an impulse I on a particle to change its speed from u to 2u. The direction of applied force and the initial velocity are opposite to each other along the same line. The work done by the force is

(a) Iu 2 3 (b) Iu 2 1 (c) I u (d) 2Iu

5. In a smooth stationary cart of length d, a small block is projected along it's length with velocity v towards front. Coefficient of restitution for each collision is e (e0) . The cart rests on a smooth ground and can move freely. The time taken by block to come to rest with respect to cart is

(a) v e ed ) 1 (  (b) e v ed ) 1 (  (c) e d (d) infinite

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)

















 

7. A ball is projected, so as to just clear two walls, the first of height 12 m at a distance 6 m from point of projection and the second of height 6 m at a distance 12 m from point of projection. Find the range (in m) of projectile.

8. A small ball is projected from point P towards a vertical wall as shown. It hits the wall when its velocity is horizontal. Ball reaches point P after one bounce on the floor. The coefficient of restitution assuming it to be same for two collisions is

2 n

. All surfaces are smooth. Find the value of n.

9. A sphere of mass m₁hits another sphere of mass m₂at rest and sticks to it. The total kinetic energy after collision is two third of their total kinetic energy before collision. Find the ratio of m₁and m2.