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: (a) 4/5ω (b) 5/4ω (c) 3/2ω (d) 2/3ω

Answer: (d). Conservation of L: 1/2MR²ω = 1/2(M+M/2)R²ω'. ω' = M/3M/2 ω = 2/3ω So the answer is (d) 2/3ω.

A thin circular disc of mass M and radius R is rotating in a… | JEE Main 2024 (8 Apr, Shift 2)

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Angular Momentum & its Conservation

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 $M/2$ is placed gently on the first disc co-axially, then the new angular velocity of the system is:

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Answer: (d)

Conservation of $L$ : $\frac{1}{2}MR^2\omega = \frac{1}{2}\left(M+\frac{M}{2}\right)R^2\omega'$ .
$\omega' = \frac{M}{3M/2}\,\omega = \frac{2}{3}\omega$
So the answer is (d) $\frac{2}{3}\omega$ .

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