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JEE Main 20248 AprilEvening Shift

Exam: JEE Main
Year: 2024
Date: 8 April
Shift: Evening Shift
Subject: Physics
Chapter: Rotational Motion

JEE Main 2024 · 8 April · Evening Shift · Physics · Rotational Motion

A thin circular disc of mass M and radius R is rotating in a...

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 :

Options

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

Correct answer

C. $\frac{2}{3} \omega$

Step-by-step solution

\begin{aligned} & \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\end{aligned}

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