Partially Elastic Collision — IISER Physics MCQs with Solutions
Free IISER Physics Partially Elastic Collision MCQs with step-by-step solutions (20 questions). Part of Collision. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Partially Elastic Collision · easy · numerical
A marble is dropped from a height of 25 m onto a hard floor. The coefficient of restitution between the marble and the floor is 3/5. To what height does the marble rise after the first bounce? (g = 10 m/s²)
A. 9 m ✓ Correct
B. 3 m
C. 15 m
D. 16 m
Solution: The rebound height is h₁ = e²h = (3/5)² × 25 = (9/25) × 25 = 9 m.
Q2 — Partially Elastic Collision · easy · numerical
A ball is dropped from a height of 50 m onto a horizontal floor. If the coefficient of restitution is 4/5, find the height reached after the first bounce. (g = 10 m/s²)
A. 20 m
B. 32 m ✓ Correct
C. 40 m
D. 16 m
Solution: h₁ = e²h = (4/5)² × 50 = (16/25) × 50 = 32 m.
Q3 — Partially Elastic Collision · easy · numerical
A ball dropped from a height of 25 m onto a floor rebounds to a height of 16 m. Find the coefficient of restitution between the ball and the floor.
A. 0.64
B. 0.6
C. 0.8 ✓ Correct
D. 0.9
Solution: e = √(h₁/h) = √(16/25) = 4/5 = 0.8.
Q4 — Partially Elastic Collision · easy · numerical
A sphere strikes a rigid wall normally at 25 m/s. If the coefficient of restitution between the sphere and the wall is 4/5, with what speed does it rebound?
A. 15 m/s
B. 25 m/s
C. 20 m/s ✓ Correct
D. 16 m/s
Solution: The rebound speed is e times the approach speed: v = (4/5) × 25 = 20 m/s.
Q5 — Partially Elastic Collision · easy · numerical
A 3 kg sphere moving at 10 m/s collides head-on with an identical stationary 3 kg sphere. The coefficient of restitution is 3/5. Find the speed of the struck sphere just after the collision.
A. 6 m/s
B. 5 m/s
C. 2 m/s
D. 8 m/s ✓ Correct
Solution: For equal masses, v₂ = u(1 + e)/2 = 10 × (8/5)/2 = 8 m/s (the incoming sphere slows to 2 m/s; 10 = 2 + 8 checks momentum).
Q6 — Partially Elastic Collision · easy · numerical
A 4 kg glider moving at 10 m/s on an air track collides head-on with an identical stationary 4 kg glider. The coefficient of restitution is 4/5. What is the speed of the incoming glider just after the collision?
A. 2 m/s
B. 5 m/s
C. 1 m/s ✓ Correct
D. 9 m/s
Solution: For equal masses, v₁ = u(1 − e)/2 = 10 × (1/5)/2 = 1 m/s, while the struck glider moves off at 9 m/s (momentum: 10 = 1 + 9).
Q7 — Partially Elastic Collision · easy · numerical
A trolley moving at 15 m/s collides head-on with a stationary trolley. After the collision the two trolleys move apart with a relative speed of 12 m/s. Find the coefficient of restitution.
A. 0.8 ✓ Correct
B. 0.75
C. 0.6
D. 0.9
Solution: e = (speed of separation)/(speed of approach) = 12/15 = 4/5 = 0.8.
Q8 — Partially Elastic Collision · easy · numerical
A ball is dropped from a height of 20 m onto a floor. The coefficient of restitution is 4/5. With what speed does the ball leave the floor after the bounce? (g = 10 m/s²)
A. 12 m/s
B. 20 m/s
C. 8 m/s
D. 16 m/s ✓ Correct
Solution: It hits the floor at √(2gh) = √(2×10×20) = 20 m/s and rebounds at e × 20 = (4/5) × 20 = 16 m/s.
Q9 — Partially Elastic Collision · medium · numerical
A puck moving at 15 m/s on frictionless ice collides head-on with an identical stationary puck. The coefficient of restitution is 3/5. Find the speed of the struck puck just after the collision.
A. 12 m/s ✓ Correct
B. 7.5 m/s
C. 3 m/s
D. 9 m/s
Solution: For equal masses, v₂ = u(1 + e)/2 = 15 × (8/5)/2 = 12 m/s; the incoming puck keeps 3 m/s, and 15 = 3 + 12 confirms momentum conservation.
Q10 — Partially Elastic Collision · medium · numerical
A 5 kg cart moving at 20 m/s collides head-on with an identical stationary 5 kg cart on a smooth track. The coefficient of restitution is 4/5. What is the speed of the originally moving cart just after the collision?
A. 2 m/s ✓ Correct
B. 4 m/s
C. 10 m/s
D. 18 m/s
Solution: For equal masses, v₁ = u(1 − e)/2 = 20 × (1/5)/2 = 2 m/s, while the struck cart moves off at 18 m/s (20 = 2 + 18).
Q11 — Partially Elastic Collision · medium · numerical
A 4 kg sphere moving at 25 m/s collides head-on with an identical stationary 4 kg sphere. The coefficient of restitution is 3/5. How much kinetic energy is lost in the collision?
A. 1250 J
B. 200 J
C. 850 J
D. 400 J ✓ Correct
Solution: The final velocities are 25(1−e)/2 = 5 m/s and 25(1+e)/2 = 20 m/s, so KE falls from ½×4×25² = 1250 J to ½×4×5² + ½×4×20² = 50 + 800 = 850 J, a loss of 400 J.
Q12 — Partially Elastic Collision · medium · numerical
A ball is dropped from a height of 25 m onto a floor with coefficient of restitution 3/5. Find the height it reaches after the SECOND bounce. (g = 10 m/s²)
A. 5.4 m
B. 1.8 m
C. 9 m
D. 3.24 m ✓ Correct
Solution: After n bounces the height is e²ⁿh, so h₂ = (3/5)⁴ × 25 = (81/625) × 25 = 3.24 m.
Q13 — Partially Elastic Collision · medium · numerical
A ball bounces on a hard floor with coefficient of restitution 3/5. What percentage of its kinetic energy is lost in each bounce?
A. 40%
B. 36%
C. 60%
D. 64% ✓ Correct
Solution: Fraction lost = 1 − e² = 1 − 9/25 = 16/25 = 64%, since the rebound KE is e² times the impact KE.
Q14 — Partially Elastic Collision · medium · numerical
A ball dropped from a height of 100 m rebounds from the floor to a height of 36 m. Find the coefficient of restitution.
A. 0.36
B. 0.6 ✓ Correct
C. 0.8
D. 0.5
Solution: e = √(h₁/h) = √(36/100) = 6/10 = 0.6.
Q15 — Partially Elastic Collision · medium · numerical
A 3 kg ball strikes a horizontal floor vertically at 25 m/s. The coefficient of restitution is 3/5. Find the magnitude of the impulse the floor exerts on the ball.
A. 120 N·s ✓ Correct
B. 30 N·s
C. 45 N·s
D. 75 N·s
Solution: The ball rebounds at e × 25 = 15 m/s, so the impulse equals the momentum change: 3 × (15 − (−25)) = 3 × 40 = 120 N·s.
Q16 — Partially Elastic Collision · medium · numerical
A 4 kg glider moving at 25 m/s on an air track collides head-on with a stationary 6 kg glider. The coefficient of restitution is 3/5. Find the speed of the 6 kg glider just after the collision.
A. 12.5 m/s
B. 10 m/s
C. 20 m/s
D. 16 m/s ✓ Correct
Solution: v₂ = m₁(1 + e)u/(m₁ + m₂) = 4 × (8/5) × 25/10 = 16 m/s; the 4 kg glider keeps 1 m/s, and 4×25 = 4×1 + 6×16 = 100 confirms momentum conservation.
Q17 — Partially Elastic Collision · medium · numerical
A 2 kg puck moving at 25 m/s on frictionless ice collides head-on with a stationary 3 kg puck. The coefficient of restitution is 4/5. Find the velocity of the 2 kg puck just after the collision.
A. 2 m/s, directed opposite to its initial motion ✓ Correct
B. 2 m/s, along its initial motion
C. 18 m/s, along its initial motion
D. 5 m/s, directed opposite to its initial motion
Solution: v₁ = (m₁ − em₂)u/(m₁ + m₂) = (2 − 0.8×3) × 25/5 = −2 m/s, i.e. it rebounds at 2 m/s while the 3 kg puck moves off at 18 m/s (momentum: 50 = −4 + 54).
Q18 — Partially Elastic Collision · medium · numerical
A 5 kg trolley moving at 20 m/s collides head-on with a stationary 3 kg trolley. After the collision the 5 kg trolley moves at 8 m/s and the 3 kg trolley at 20 m/s, both in the original direction. Find the coefficient of restitution.
A. 0.8
B. 0.6 ✓ Correct
C. 0.75
D. 0.4
Solution: e = (speed of separation)/(speed of approach) = (20 − 8)/(20 − 0) = 12/20 = 0.6 (momentum checks: 5×20 = 5×8 + 3×20 = 100).
Q19 — Partially Elastic Collision · medium · numerical
A 1 kg ball is dropped from a height of 75 m onto a floor. The coefficient of restitution is 4/5. How much kinetic energy is lost in the first bounce? (g = 10 m/s²)
A. 270 J ✓ Correct
B. 480 J
C. 150 J
D. 750 J
Solution: KE at impact = mgh = 1×10×75 = 750 J; the rebound KE is e² × 750 = 0.64 × 750 = 480 J, so 270 J is lost.
Q20 — Partially Elastic Collision · medium · numerical
A 4 kg cart moving at 15 m/s strikes a rigid wall head-on and rebounds. The coefficient of restitution between the cart and the wall is 3/5. How much kinetic energy is lost in the impact?
A. 144 J
B. 288 J ✓ Correct
C. 162 J
D. 450 J
Solution: The cart rebounds at e × 15 = 9 m/s, so KE falls from ½×4×15² = 450 J to ½×4×9² = 162 J, a loss of 288 J.