JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Conservation of Momentum

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A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be:

(A) $1 : 1$
(B) $2 : 1$ ✓ Correct
(C) $1 : 4$
(D) $4 : 1$

Answer: (B)

Solution

Kinetic energy is related to momentum by

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

. For equal kinetic energies:

\frac{P _{1}^{2}}{2 m _{1}} = \frac{P _{2}^{2}}{2 m _{2}}

. This gives

\frac{P _{1}^{2}}{P _{2}^{2}} = \frac{m _{1}}{m _{2}} = \frac{8}{2} = 4

. Therefore,

\frac{P _{1}}{P _{2}} = 2

, or the ratio is

2 : 1

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Single correct option

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