Practice portal › Work, Energy and Power › Kinetic Energy and Momentum

Two bodies are having kinetic energies in the ratio 16:9. If they have same linear momentum, the ratio of their masses respectively is

Asked in JEE Main 13th April 1st Shift 2023 · Relating kinetic energy to momentum

(1) 4 : 3
(2) 3 : 4
(3) 16 : 9
(4) 9 : 16

Answer: (4) 9 : 16

Step-by-step solution

K=(p²)/(2m), so at equal p, m∝1/K.

(m₁)/(m₂)=(K₂)/(K₁)=9/(16).

Why the other options are wrong

(1) Comes from taking a square root that is not there and also forgetting to invert.
(2) Comes from taking a square root that is not there; m is inversely proportional to K itself.
(3) Comes from forgetting to invert: the body with more kinetic energy at the same momentum is the lighter one.

More Kinetic Energy and Momentum questions

All Kinetic Energy and Momentum questions →

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.

Practise this with a timer