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C.B.S.E. SUBJECTIVE LEVEL - I (REVIEW YOUR CONCEPTS) 1. Two solid spheres of radii 6 cm and 12 cm and masses 36 g & 18 g respectively touch each other. What is the position of centre of mass of the combination? 2. A projectile is fired with a speed u at an angle above a horizontal field. The coefficient of restitu- tion of collision between the projectile and the field is e. How far from the starting point, does the projectile makes its second collision with the field? 3. Prove that the CM of two particles lies between the particles on a line that connects the two par- ticles. 4. A 3 kg mass moving at a speed of 15 ms-1 collides with a 6 kg object initially at rest. They stick together. Find the velocity of the combination after the collision. 5. Two ice skaters, A and B, approach each other at right angles. Skater A has a mass of 50 kg and she is traveling in the + x direction at 2 ms-1. Skater B has a mass of 40 kg and he is moving in the + y direction at 2.5 ms-1. They collide and cling together. Find the final velocity of the couple. 6. A block of mass m moving at a speed v collides with another block of mass 2m at rest. The lighter block comes to rest after collision. What is the coefficient of restitution. 7. A particle is dropped on a surface from a height of 20 m. If the coefficient of restitution is 0.5, what is the total distance covered by the particle before coming to rest. 8. A rocket had an initial mass of 2.72 x 106 kg and a final mass of 2.52 x 106 kg after the fuel was burnt and the gases were expelled at the rate of 1290 kg/s (a) Find the time of complete burning of fuel (b) Find the maximum velocity if v = 55000 m/s and g = 9.8 m/s2. where vr = velocity of ejected gas with respect to the rocket. 9. A ball of mass m is dropped onto a floor from a certain height. The collision is perfectly elastic and the ball rebounds to the same height and again falls. Find the average force exerted by the ball on the floor during long time interval. 10. A body of mass m makes an elastic collision with another identical body at rest. Show that if the collision is not head on, the bodies go at right angle to each other after the collision. 11. A rocket of initial mass 10000 kg ejects gasses at a constant rate of 30 kgs-1 with a relative speed of 5 kms-1. Neglecting gravity, what is the acceleration of the rocket one minute after the blast of rocket : 12 Answer carefully, with reasons : (a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact) ? (b) Is the total linear momentum conserved during the short time of an elastic collision to two balls? (c) What are the answers to (a) and (b) for an inelastic collision ? (d) If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic ? (Note, we are talking here of potential energy cor

- 1. C.B.S.E. SUBJECTIVE LEVEL - I (REVIEW YOUR CONCEPTS) 1. Two solid spheres of radii 6 cm and 12 cm and masses 36 g & 18 g respectively touch each other. What is the position of centre of mass of the combination? 2. A projectile is fired with a speed u at an angle above a horizontal field. The coefficient of restitu- tion of collision between the projectile and the field is e. How far from the starting point, does the projectile makes its second collision with the field? 3. Prove that the CM of two particles lies between the particles on a line that connects the two par- ticles. 4. A 3 kg mass moving at a speed of 15 ms-1 collides with a 6 kg object initially at rest. They stick together. Find the velocity of the combination after the collision. 5. Two ice skaters, A and B, approach each other at right angles. Skater Ahas a mass of 50 kg and she is traveling in the + x direction at 2 ms-1 . Skater B has a mass of 40 kg and he is moving in the + y direction at 2.5 ms-1 . They collide and cling together. Find the final velocity of the couple. 6. A block of mass m moving at a speed v collides with another block of mass 2m at rest. The lighter block comes to rest after collision. What is the coefficient of restitution. 7. A particle is dropped on a surface from a height of 20 m. If the coefficient of restitution is 0.5, what is the total distance covered by the particle before coming to rest. 8. A rocket had an initial mass of 2.72 x 106 kg and a final mass of 2.52 x 106 kg after the fuel was burnt and the gases were expelled at the rate of 1290 kg/s (a) Find the time of complete burning of fuel (b) Find the maximum velocity if vr = 55000 m/s and g = 9.8 m/s2 . where vr = velocity of ejected gas with respect to the rocket. 9. A ball of mass m is dropped onto a floor from a certain height. The collision is perfectly elastic and the ball rebounds to the same height and again falls. Find the average force exerted by the ball on the floor during long time interval. 10. A body of mass m makes an elastic collision with another identical body at rest. Show that if the collision is not head on, the bodies go at right angle to each other after the collision. 11. A rocket of initial mass 10000 kg ejects gasses at a constant rate of 30 kgs-1 with a relative speed of 5 kms-1 . Neglecting gravity, what is the acceleration of the rocket one minute after the blast of rocket : 12 Answer carefully, with reasons : (a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact) ? (b) Is the total linear momentum conserved during the short time of an elastic collision to two balls? (c) What are the answers to (a) and (b) for an inelastic collision ?
- 2. (d) If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic ? (Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy). 13 A molecule in a gas container hits a horizontal wall with speed 200 ms-1 and 300 with the normal, and rebounds with the same speed. Is momentum conserved in the collision ? Is the collision elastic or inelastic ? 14 The bob A of a pendulum released from 300 to the vertical hits another bob B of the same mass at rest on a table as shown in fig. How high does the bob A rise after the collision ? Neglect the size of the bobs and assume the collision to be elastic. A B m m 300 15 A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, sand starts leaking out of a hole on the trolley’s floor at the rate of 0.05 kg s-1 . What is the speed of the trolley after the entire sand bag is empty ?