Physics-DPP-2-3.CENTRE OF MASS, CONSERVATION OF MOMENTUM, COLLISION

PHYSICS Topic: CENTRE OF MASS, CONSERVATION OF MOMENTUM, COLLISION Date: r 1. A particle of mass 15 kg an initial velocity v = iˆ - 2ˆjm / s . It collides with another body and the impact time is 0.1 s, resulting in a r velocity v = 6iˆ + 4ˆj + 5kˆ m / s after impact. The average force of impact on the particle is : (a) 15 | 5iˆ + 6 ˆj + 5kˆ | (b) 15 | 5iˆ + 6 ˆj - 5kˆ | (c) 150 | 5iˆ - 6 ˆj + 5kˆ | (d) 150 | 5iˆ + 6 ˆj + 5kˆ | 2. A man of mass M stands at one end of a plank of length L which lies at rest on a frictionless surface. The man walks to the other end M of the plank. If the mass of the plank is 3 , the distance that the man moves relative to the ground is : (a) 3L 4 (b) L 4 (c) 4 L L 5 (d) 3 3. Two ice skaters A and B approach each other at right angles. Skater A has a mass 30 kg and velocity 1 m/s skater B has a mass 20 kg and velocity 2 m/s. They meet and cling together. Their final velocity of the couple is : (a) 2 m/s (b) 1.5 m/s (c) 1 m/s (d) 2.5 m/s 4. Three rods of the same mass are placed as shown in the figure. What will be the co-ordinate of centre of mass of the system? æça a ö÷ æç a , a ö÷ 2a 2a æça a ö÷ (a) çè , ÷ (b) ç ÷ (c) , (d) ç , ÷ 2 2 ø è 2 ø 3 3 è3 3 ø 5. In a gravity free space, a man of mass M standing at a height h above the floor, throws a ball of mass m straight down with a speed u. When the ball reaches the floor, the distance of the man above the floor with be : çæ m ö÷ çæ Mö÷ m (a) hç1+ ÷ (b) ç1+ ÷h (c) h (d) h è Mø è m ø M r ˆ 6. Two particles of equal mass have co-ordinates (2m, 4m, 6m) and (6m, 2m, 8m). Of these one particle has a velocity v1 = (2i )m / s and r ˆ another particle has velocity v2 = (2 j)m / s at time t = 0. The coordinate of their centre of mass at time t = 1 s will be : (a) (4m, 4m, 7m) (b) (5m, 4m, 7m) (c) (2m, 4m, 6m) (d) (4m, 5m, 4m) 7. A 2 kg of block of wood rests on a long table top. A 5g bullet moving horizontally with a speed of 150 m/s is shot into the block and sticks to it. The block then slides 2.7 m along the table top and comes to a stop. The force of friction between the block and the table is : (a) 0.052 N (b) 3.63 N (c) 2.50 N (d) 1.04 N PHYSICS Topic: CENTRE OF MASS, CONSERVATION OF MOMENTUM, COLLISION Date: 8. The collision of two balls of equal mass takes place at the origin of co-ordinates. Before collision, the components of velocities are (vx = 50 cm/s, vy = 0) and (vx = – 40 cm/s and vy = 30 cm/s). The first ball comes to rest after collision. The velocity components (vx and vy respectively) of the second ball are : (a) 10 and 30 cm/s (b) 30 and 10 cm/s (c) 5 and 15 cm/s (d) 15 and 5 cm/s 9. A shell is fired from cannon with a velocity v at an angle θ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon and the spread (in ms –1) of the other piece immediately after the explosion is : (a) 3v cosθ (b) 2v cosθ (c) 3 v cosθ 2 (d) 3 v cosθ 2 10. A sphere of mass m moving with a constant velocity u hits another stationary sphere of same mass. If e is the coefficient of v1 restitution, then ratio of velocities of the two spheres after collision will be : 2 1- e 1+ e e + 1 e - 1 (a) 1+ e (b) 1- e (c) e - 1 (d) e + 1 PHYSICS Topic: CENTRE OF MASS, CONSERVATION OF MOMENTUM, COLLISION Date: Answer Key 1. (d) 2. (b) 3. (c) 4. (d) 5. (a) 6. (b) 7. (a) 8. (a) 9. (a) 10. (b)