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Class 11  »  Physics  »  Work Energy and Power

Coefficient of Restitution - UNSOLVED PRACTICE SET

Class 11

Chapter: Work Energy and Power | Topic: Coefficient of Restitution

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Class 11

COEFFICIENT OF RESTITUTION - UNSOLVED PRACTICE SET

Topic: Coefficient of Restitution

Time: 40 mins | Marks: 30 | Difficulty: Medium

Multiple Choice Questions

Q1. The coefficient of restitution e is defined as:

  1. The ratio of initial velocities to final velocities
  2. The ratio of relative velocity of separation to relative velocity of approach
  3. The ratio of kinetic energies after and before collision
  4. The ratio of masses of colliding bodies

Q2. For a perfectly elastic collision:

  1. e = 0
  2. 0 < e < 1
  3. e = 1
  4. e > 1

Q3. For a perfectly inelastic collision:

  1. e = 0
  2. e = 1
  3. e = 0.5
  4. e = ∞

Q4. A ball dropped from height h rebounds to height h/4. The coefficient of restitution is:

  1. 1/4
  2. 1/2
  3. 1/√2
  4. √2

Q5. In a collision where e = 0.8:

  1. 80% of kinetic energy is conserved
  2. The relative speed of separation is 80% of the relative speed of approach
  3. 80% of momentum is conserved
  4. The collision is perfectly elastic

Q6. The coefficient of restitution depends on:

  1. The masses of the colliding bodies
  2. The velocities of the colliding bodies
  3. The materials and nature of the colliding surfaces
  4. The angle of collision only

Short Answer Questions

Q7. Define coefficient of restitution. Write its mathematical expression for a one-dimensional collision.

Q8. A ball is dropped from 10 m and rebounds to 6.4 m. Calculate the coefficient of restitution between the ball and the ground.

Q9. Two bodies collide with coefficient of restitution 0.5. If the relative velocity of approach is 20 m/s, what is the relative velocity of separation?

Q10. In your school, a student drops a superball and a tennis ball from the same height. The superball rebounds to 80% of its drop height, while the tennis ball rebounds to 50%. Calculate e for each ball and explain which is more elastic.

Q11. Show that for a ball dropped from height h and rebounding to height h', the coefficient of restitution is e = √(h'/h).

Q12. Why is the coefficient of restitution always between 0 and 1 for ordinary materials? What would e > 1 imply?

Long Answer Questions

Q13. Define coefficient of restitution and derive its relationship with the heights of fall and rebound. Show that for a ball dropped from height H and making multiple bounces:

(a) The total distance travelled before coming to rest is H(1 + e²)/(1 − e²)

(b) The total time of motion is √(2H/g) × (1 + e)/(1 − e)

Derive these expressions step by step.

Q14. Two smooth spheres A and B of masses 2 kg and 3 kg moving with velocities 4 m/s and 2 m/s respectively in the same direction collide. After collision, A moves at 1 m/s in the same direction.

(a) Calculate the velocity of B after collision.

(b) Calculate the coefficient of restitution.

(c) Calculate the kinetic energy before and after collision.

(d) Calculate the percentage loss in kinetic energy.

(e) Classify the collision based on the value of e.

Q15. Discuss the physics of bouncing balls:

(a) Derive the expression for the height after n bounces

(b) Derive the expression for the velocity after n bounces

(c) Show that the ball eventually comes to rest

(d) Explain where the "lost" kinetic energy goes

(e) Discuss how temperature affects the coefficient of restitution

Application-Based Problems

Q16. A ball is dropped from a height of 20 m onto a concrete floor. The coefficient of restitution is 0.8.

(a) Calculate the height after the first bounce.

(b) Calculate the height after the second bounce.

(c) Calculate the total distance travelled by the ball before coming to rest.

(d) Calculate the total time taken before coming to rest. (Take g = 10 m/s²)

(e) What would be the answers if e = 1? Discuss the physical significance.

Q17. In a school experiment, two balls A and B of masses 0.5 kg and 0.3 kg collide on a frictionless track. Before collision, A moves at 4 m/s and B moves at 2 m/s in the opposite direction. After collision, A moves at 1 m/s in its original direction.

(a) Calculate the velocity of B after collision.

(b) Calculate the coefficient of restitution.

(c) Calculate the impulse on each ball.

(d) Verify that momentum is conserved.

(e) If e were 1 (perfectly elastic), what would be the velocities after collision?

Q18. A steel ball bearing is dropped from 2 m onto a steel plate. The coefficient of restitution is measured to be 0.95.

(a) Calculate the rebound height.

(b) Calculate the time interval between the first and second impact.

(c) Calculate the number of bounces before the rebound height is less than 1 cm.

(d) Calculate the total distance travelled.

(e) Design an experiment to measure e for different materials (wood, rubber, glass) using this setup.


Total: 30 Marks | Time: 40 mins

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