A thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity ω . If another disc of same dimensions but of mass M / 2 is placed gently on the first disc co-axially, then the new angular velocity of the system is :

Physics · Rotational Dynamics

JEE Main 2024 — 8 April, Shift 2 — Question 33

A thin circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$ . If another disc of same dimensions but of mass $\mathrm{M} / 2$ is placed gently on the first disc co-axially, then the new angular velocity of the system is :

Option A:
$\frac{4}{5} \omega$
Option B:
$\frac{5}{4} \omega$
Option C:
$\frac{2}{3} \omega$
Correct
Option D:
$\frac{3}{2} \omega$

Answer: C

Step-by-step solution

$\mathrm{I}_{1} \omega=\mathrm{I}_{2} \omega_{2}$

$\frac{\mathrm{MR}^{2}}{2} \omega=\frac{3}{2}\left(\frac{\mathrm{MR}^{2}}{2}\right) \omega_{2}$

$\omega_{2}=\frac{2}{3} \omega$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 8 April, Shift 2
Subject: Physics
Chapter: Rotational Dynamics
Topic: Angular Momentum and its Conservation