A thin uniform circular disc of mass ' M ' and radius ' R ' is… | MHT CET 2023 (12 May, Shift 1)

Q40MHT CET 2023 · 12 MAY · SHIFT 1Medium

Angular Momentum & its Conservation

A thin uniform circular disc of mass ' $M$ ' and radius ' $R$ ' is rotating with angular velocity ' $\omega$ ', in a horizontal plane about an axis passing through its centre and perpendicular to its plane. Another disc of same radius but of mass $\left(\frac{M}{2}\right)$ is placed gently on the first disc co-axially. The new angular velocity will be

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Answer: (a)

Angular momentum is conserved: $I_1\omega = (I_1+I_2)\omega'$ .
Both discs have $I = \frac{1}{2}(\text{mass})R^2$ , so $\omega' = \frac{M}{M + M/2}\,\omega$ .
$\omega' = \frac{2}{3}\omega$
So the answer is (a) $\frac{2}{3}\omega$ .

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