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Collision — IISER Physics MCQs with Solutions
Free IISER Physics Collision MCQs with step-by-step solutions covering Elastic Collision, Inelastic Collision, Partially Elastic Collision. Practise online on Prepizo — no login needed.
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Sample questions with solutions
Q1 — Elastic Collision · easy · numerical
Two identical 2 kg gliders are on a frictionless air track. One glider moving at 14 m/s collides head-on elastically with the other, which is at rest. What is the speed of the struck glider just after the collision?
A. 7 m/s
B. 28 m/s
C. 0 m/s
D. 14 m/s ✓ Correct
Solution: In a head-on elastic collision between equal masses the velocities are exchanged: the moving glider stops and the struck glider moves off at 14 m/s.
Q2 — Elastic Collision · easy · numerical
A puck sliding at 25 m/s on frictionless ice collides head-on elastically with an identical stationary puck. What is the speed of the incoming puck just after the collision?
A. 12.5 m/s
B. 0 m/s ✓ Correct
C. 5 m/s
D. 25 m/s
Solution: Equal masses exchange velocities in a head-on elastic collision, so the incoming puck comes to rest (0 m/s) and the other moves off at 25 m/s.
Q3 — Elastic Collision · easy · numerical
A 9 kg sphere moving at 8 m/s collides head-on elastically with a stationary 3 kg sphere. Find the speed of the 3 kg sphere after the collision.
A. 8 m/s
B. 6 m/s
C. 4 m/s
D. 12 m/s ✓ Correct
Solution: v₂ = 2m₁u/(m₁+m₂) = 2×9×8/12 = 12 m/s, while the 9 kg sphere continues at 4 m/s; momentum 72 = 9×4 + 3×12 is conserved.
Q4 — Elastic Collision · easy · numerical
A 10 kg trolley moving at 12 m/s collides head-on elastically with a stationary 5 kg trolley. What is the velocity of the 10 kg trolley after the collision?
A. 16 m/s
B. 8 m/s
C. 6 m/s
D. 4 m/s ✓ Correct
Solution: v₁ = (m₁−m₂)u/(m₁+m₂) = 5×12/15 = 4 m/s in the original direction, while the 5 kg trolley moves off at 16 m/s.
Q5 — Elastic Collision · easy · numerical
A 3 kg cart moving at 15 m/s collides head-on elastically with a stationary 6 kg cart. Find the speed of the 6 kg cart after the collision.
A. 5 m/s
B. 10 m/s ✓ Correct
C. 15 m/s
D. 7.5 m/s
Solution: v₂ = 2m₁u/(m₁+m₂) = 2×3×15/9 = 10 m/s; the 3 kg cart rebounds at 5 m/s, and momentum 45 = −15 + 60 checks out.
Q6 — Elastic Collision · easy · numerical
A 12 kg sphere moving at 6 m/s collides head-on elastically with a stationary 4 kg sphere. What speed does the 4 kg sphere acquire?
A. 4.5 m/s
B. 6 m/s
C. 3 m/s
D. 9 m/s ✓ Correct
Solution: v₂ = 2m₁u/(m₁+m₂) = 2×12×6/16 = 9 m/s, while the 12 kg sphere slows to 3 m/s (momentum 72 = 36 + 36).
Q7 — Elastic Collision · easy · numerical
A neutron makes a head-on elastic collision with a stationary proton, whose mass is nearly equal to its own. What percentage of the neutron's kinetic energy is transferred to the proton?
A. 25%
B. 50%
C. 75%
D. 100% ✓ Correct
Solution: Fraction transferred = 4m₁m₂/(m₁+m₂)²; with m₁ ≈ m₂ this equals 4m²/4m² = 1, so essentially 100% of the kinetic energy is handed over.
Q8 — Elastic Collision · easy · numerical
A 1 kg marble moving at 16 m/s collides head-on elastically with a very heavy stationary sphere. With what speed does the marble rebound?
A. 0 m/s
B. 32 m/s
C. 8 m/s
D. 16 m/s ✓ Correct
Solution: When m₂ ≫ m₁, v₁ = (m₁−m₂)u/(m₁+m₂) ≈ −u, so the marble simply bounces back with nearly its original speed of 16 m/s.
Q9 — Inelastic Collision · easy · numerical
A 4 kg glider moving at 9 m/s on a frictionless air track collides with a stationary 8 kg glider and the two couple together. Find their common speed just after the collision.
A. 6 m/s
B. 2 m/s
C. 3 m/s ✓ Correct
D. 4.5 m/s
Solution: Momentum conservation gives v = m₁u/(m₁+m₂) = 4×9/12 = 3 m/s.
Q10 — Inelastic Collision · easy · numerical
A 5 kg trolley moving at 12 m/s on a smooth horizontal track collides with a stationary 10 kg trolley and sticks to it. What is the speed of the combination just after impact?
A. 8 m/s
B. 6 m/s
C. 4 m/s ✓ Correct
D. 3 m/s
Solution: v = m₁u/(m₁+m₂) = 5×12/15 = 4 m/s, since the total momentum 60 kg·m/s is shared by 15 kg.
Q11 — Inelastic Collision · easy · numerical
A 6 kg puck sliding at 12 m/s on frictionless ice hits a stationary 2 kg puck and the two move off together. Find their common speed.
A. 9 m/s ✓ Correct
B. 4.5 m/s
C. 6 m/s
D. 12 m/s
Solution: v = m₁u/(m₁+m₂) = 6×12/8 = 72/8 = 9 m/s by conservation of momentum.
Q12 — Inelastic Collision · easy · numerical
A 4 kg cart moving at 15 m/s catches up with an 8 kg cart moving at 6 m/s in the same direction on a smooth track. They collide and lock together. Find their common speed after the collision.
A. 12 m/s
B. 9 m/s ✓ Correct
C. 10.5 m/s
D. 7.5 m/s
Solution: v = (4×15 + 8×6)/(4+8) = 108/12 = 9 m/s; total momentum 108 kg·m/s is conserved.
Q13 — Inelastic Collision · easy · numerical
A 6 kg sphere moving at 5 m/s collides head-on with a 4 kg sphere moving at 10 m/s in the opposite direction. They stick together on impact. Find the velocity of the combined mass just after the collision.
A. 1 m/s, in the direction the 6 kg sphere was moving
B. 1 m/s, in the direction the 4 kg sphere was moving ✓ Correct
C. 3 m/s, in the direction the 4 kg sphere was moving
D. 7 m/s, in the direction the 6 kg sphere was moving
Solution: Taking the 6 kg sphere's direction as positive, v = (6×5 − 4×10)/10 = −10/10 = −1 m/s, i.e. 1 m/s along the 4 kg sphere's original direction.
Q14 — Inelastic Collision · easy · numerical
A 2 kg glider moving at 10 m/s and a 5 kg glider moving at 4 m/s approach each other head-on on a frictionless air track. They collide and couple together. What is their speed just after the collision?
A. 2 m/s
B. 0 m/s ✓ Correct
C. 7 m/s
D. 4 m/s
Solution: The net momentum is 2×10 − 5×4 = 0, so the coupled gliders come to rest: v = 0/7 = 0 m/s.
Q15 — Inelastic Collision · easy · numerical
A 50 g pellet moving horizontally at 200 m/s embeds itself in a 1.95 kg cart resting on a smooth horizontal track. Find the speed of the cart (with the pellet) just after the impact.
A. 2.5 m/s
B. 10 m/s
C. 5 m/s ✓ Correct
D. 4 m/s
Solution: Momentum conservation: 0.05×200 = (0.05 + 1.95)v, so v = 10/2 = 5 m/s.
Q16 — Inelastic Collision · easy · numerical
A 10 kg cart moving at 6 m/s collides with a stationary 2 kg cart and the two stick together. How much kinetic energy is lost in the collision?
A. 60 J
B. 180 J
C. 150 J
D. 30 J ✓ Correct
Solution: v = 10×6/12 = 5 m/s, so KE falls from ½×10×6² = 180 J to ½×12×5² = 150 J, a loss of 30 J.
Q17 — 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.
Q18 — 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.
Q19 — 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.
Q20 — 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.
Q21 — 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).
Q22 — 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).
Q23 — 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.
Q24 — 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.
Q25 — Elastic Collision · medium · numerical
A 4 kg trolley moving at 10 m/s collides head-on elastically with a 2 kg trolley moving toward it at 5 m/s. Find the speed of the 2 kg trolley after the collision.
A. 15 m/s ✓ Correct
B. 10 m/s
C. 20 m/s
D. 5 m/s
Solution: v₂ = (2m₁u₁ + (m₂−m₁)u₂)/(m₁+m₂) = (2×4×10 + (−2)(−5))/6 = 90/6 = 15 m/s; the 4 kg trolley comes to rest, and momentum 40 − 10 = 30 = 2×15 is conserved.
Q26 — Elastic Collision · medium · numerical
A 3 kg puck moving at 20 m/s strikes a stationary 9 kg puck head-on elastically. What fraction of the incident kinetic energy is transferred to the 9 kg puck?
A. 8/9
B. 1/4
C. 3/4 ✓ Correct
D. 1/2
Solution: Fraction transferred = 4m₁m₂/(m₁+m₂)² = 4×3×9/12² = 108/144 = 3/4; indeed the 9 kg puck moves at 10 m/s, carrying 450 J of the initial 600 J.
Q27 — Elastic Collision · medium · numerical
A 4 kg sphere moving at 16 m/s collides head-on elastically with a stationary 12 kg sphere. What fraction of its kinetic energy does the 4 kg sphere retain after the collision?
A. 1/2
B. 1/4 ✓ Correct
C. 1/16
D. 3/4
Solution: Retained fraction = ((m₁−m₂)/(m₁+m₂))² = (8/16)² = 1/4; the 4 kg sphere rebounds at 8 m/s, so its KE falls from 512 J to 128 J.
Q28 — Elastic Collision · medium · numerical
A 12 kg cart moving at 9 m/s collides head-on elastically with a stationary cart of negligibly small mass. With what speed does the light cart move off?
A. 13.5 m/s
B. 18 m/s ✓ Correct
C. 9 m/s
D. 4.5 m/s
Solution: When m₁ ≫ m₂, v₂ = 2m₁u/(m₁+m₂) ≈ 2u = 2×9 = 18 m/s, while the heavy cart barely slows down.
Q29 — Elastic Collision · medium · numerical
A marble moving at 25 m/s strikes an identical stationary marble a glancing elastic blow, after which the two move at right angles to each other. If one marble moves off at 15 m/s, find the speed of the other.
A. 15 m/s
B. 20 m/s ✓ Correct
C. 5 m/s
D. 10 m/s
Solution: For equal masses in an elastic collision, kinetic energy conservation gives u² = v₁² + v₂², so v₂ = √(25² − 15²) = √400 = 20 m/s.
Q30 — Elastic Collision · medium · numerical
A 2 kg glider moving at 12 m/s on an air track collides head-on elastically with a stationary 10 kg glider. With what speed does the 2 kg glider rebound?
A. 12 m/s
B. 8 m/s ✓ Correct
C. 6 m/s
D. 4 m/s
Solution: v₁ = (m₁−m₂)u/(m₁+m₂) = (−8)×12/12 = −8 m/s, i.e. a rebound at 8 m/s; the 10 kg glider moves forward at 4 m/s (momentum 24 = −16 + 40).