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JEE Main 20248 AprilMorning Shift

Exam: JEE Main
Year: 2024
Date: 8 April
Shift: Morning Shift
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

JEE Main 2024 · 8 April · Morning Shift · Physics · Center of Mass, Momentum and Collision

Three bodies A, B and C have equal kinetic energies and their...

Three bodies A, B and C have equal kinetic energies and their masses are

400 \mathrm{~g}

.

1.2 \mathrm{~kg}

and

1.6 \mathrm{~kg}

respectively. The ratio of their linear momenta is :

Options

A $\sqrt{2} ; \sqrt{3} ; 1$
B $1: \sqrt{3}: 2$
C $1: \sqrt{3}: \sqrt{2}$
D $\sqrt{3}: \sqrt{2}: 1$

Correct answer

B. $1: \sqrt{3}: 2$

Step-by-step solution

\begin{aligned} & \mathrm{KE}=\frac{\mathrm{P}^2}{2 \mathrm{~m}} \\ & \mathrm{P} \propto \sqrt{\mathrm{m}}\end{aligned}

Hence,

\mathrm{P}_{\mathrm{A}}: \mathrm{P}_{\mathrm{B}}: \mathrm{P}_{\mathrm{C}} =\sqrt{400}: \sqrt{1200}: \sqrt{1600}=1: \sqrt{3}: 2

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