JEE Main 2023 · 13 April · morning · Single correct · +4 / −1
Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is :
- (a) 3: 4
- (b) 4: 3
- (c) 9: 16
- (d) 16: 9
Answer and solution
Answer (c) 9: 16
Solution
Physics sir · 3 steps
Same momentum means K = p²/2m, so kinetic energy goes as one over mass: just flip the ratio.
- Link K and p. Write K = 1/2mv² and p = mv. Substituting v = p/m gives a form with no velocity in it.
K = p²/2m
- Same momentum. With p the same for both bodies, K ∝ 1/m. So K₁/K₂ = m₂/m₁, which gives m₁/m₂ = K₂/K₁ = 9/16.
- So. The ratio of their masses is 9 : 16, option (c). The lighter body must move faster to carry the same momentum, so it has more kinetic energy.
The idea to keep. Whenever momentum is fixed, use K = p²/2m: kinetic energy is inversely proportional to mass. If mass is fixed instead, K ∝ p².
Answer from the NTA final answer key. Solution by PrepWiser.