Rotational Motion

JEE Main level, single correct, medium

200 of 280

Question 200 of 280

A thin circular disc of mass MM and radius RR is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity ω\omega. If another disc of same dimensions but of mass M/2\mathrm{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: (C) 23ω\frac{2}{3} \omega

I1ω=I2ω2MR22ω=32(MR22)ω2ω2=23ω\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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