Three bodies A , B and C have equal kinetic energies and their masses are 400 g , 1.2 kg and 1.6 kg respectively. The ratio of their linear momenta is :

Physics · Work, Power & Energy

JEE Main 2024 — 8 April, Shift 1 — Question 31

Three bodies $\mathrm{A}, \mathrm{B}$ and C have equal kinetic energies and their masses are $400 \mathrm{~g}, 1.2 \mathrm{~kg}$ and 1.6 kg respectively. The ratio of their linear momenta is :

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

Answer: A

Step-by-step solution

$\mathrm{KE}=\frac{\mathrm{P}^{2}}{2 \mathrm{~m}}$

$\mathrm{P} \propto \sqrt{\mathrm{m}}$

Hence, $\mathrm{P}_{\mathrm{A}}: \mathrm{P}_{\mathrm{B}}: \mathrm{P}_{\mathrm{C}}$

$=\sqrt{400}: \sqrt{1200}: \sqrt{1600}=1: \sqrt{3}: 2$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 8 April, Shift 1
Subject: Physics
Chapter: Work, Power & Energy
Topic: Kinetic Energy and Work-Energy Theorem