Elastic Collision — IISER Physics MCQs with Solutions
Free IISER Physics 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 — 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 — 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.
Q10 — 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.
Q11 — 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.
Q12 — 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.
Q13 — 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.
Q14 — 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).
Q15 — Elastic Collision · medium · numerical
A 6 kg cart moving at 10 m/s catches up with a 2 kg cart moving at 2 m/s in the same direction and collides with it elastically. Find the speed of the 2 kg cart after the collision.
A. 14 m/s ✓ Correct
B. 8 m/s
C. 10 m/s
D. 12 m/s
Solution: v₂ = (2m₁u₁ + (m₂−m₁)u₂)/(m₁+m₂) = (2×6×10 − 4×2)/8 = 112/8 = 14 m/s; the 6 kg cart slows to 6 m/s, and momentum 60 + 4 = 36 + 28 is conserved.
Q16 — Elastic Collision · medium · numerical
An 8 kg glider moving at 15 m/s collides head-on elastically with a stationary glider and continues in the same direction at 5 m/s (one-third of its original speed). Find the mass of the second glider.
A. 2 kg
B. 4 kg ✓ Correct
C. 6 kg
D. 8 kg
Solution: v₁/u = (m₁−m₂)/(m₁+m₂) = 1/3 gives 3(8 − m) = 8 + m, so m = 4 kg; the struck glider then moves off at 20 m/s (momentum 120 = 40 + 80).
Q17 — Elastic Collision · medium · numerical
An 8 kg sphere moving at 10 m/s collides head-on elastically with a stationary 2 kg sphere. How much kinetic energy does the 2 kg sphere carry away?
A. 144 J
B. 200 J
C. 400 J
D. 256 J ✓ Correct
Solution: v₂ = 2m₁u/(m₁+m₂) = 2×8×10/10 = 16 m/s, so KE₂ = ½×2×16² = 256 J of the initial 400 J (the 8 kg sphere keeps 144 J, moving at 6 m/s).
Q18 — Elastic Collision · medium · numerical
A 2 kg puck moving at 15 m/s strikes a stationary 3 kg puck head-on elastically. What percentage of the incident kinetic energy is transferred to the 3 kg puck?
A. 96% ✓ Correct
B. 50%
C. 75%
D. 84%
Solution: Fraction transferred = 4m₁m₂/(m₁+m₂)² = 4×2×3/25 = 24/25 = 96%; the 3 kg puck moves at 12 m/s, carrying 216 J of the initial 225 J.
Q19 — Elastic Collision · medium · numerical
A 5 kg trolley moving at 9 m/s collides head-on elastically with a stationary 10 kg trolley. Find the magnitude of the impulse delivered to the 10 kg trolley.
A. 30 N·s
B. 90 N·s
C. 45 N·s
D. 60 N·s ✓ Correct
Solution: v₂ = 2m₁u/(m₁+m₂) = 2×5×9/15 = 6 m/s, so the impulse is m₂v₂ = 10×6 = 60 N·s; the 5 kg trolley rebounds at 3 m/s, matching momentum 45 = −15 + 60.
Q20 — Elastic Collision · medium · numerical
A 4 kg sphere moving at 18 m/s collides head-on elastically with a stationary 8 kg sphere. What is the speed of separation of the two spheres after the collision?
A. 12 m/s
B. 9 m/s
C. 6 m/s
D. 18 m/s ✓ Correct
Solution: In an elastic collision the speed of separation equals the speed of approach, 18 m/s; explicitly v₁ = −6 m/s and v₂ = 12 m/s, and 12 − (−6) = 18 m/s.