JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Conservation of 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 :

(A) $4 : 3$
(B) $3 : 4$
(C) $16 : 9$
(D) $9 : 16$ ✓ Correct

Answer: (D)

Solution

For a body with momentum

p

and mass

m

, the kinetic energy is

K = \frac{p ^{2}}{2 m}

.

Given that both bodies have the same momentum

p

and their kinetic energies are in the ratio

16 : 9

\frac{K _{1}}{K _{2}} = \frac{p ^{2} / ( 2 m _{1} )}{p ^{2} / ( 2 m _{2} )} = \frac{m _{2}}{m _{1}} = \frac{16}{9}

Therefore:

\frac{m _{1}}{m _{2}} = \frac{9}{16}

The ratio of masses is

9 : 16

JEE Main · 2023 · 13 Apr 2023 · Shift 1 · Single correct option

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