Rotational Motion

JEE Main level, single correct, medium

242 of 280

Question 242 of 280

Initial angular velocity of a circular disc of mass MM is ω1\omega_1. Then two small spheres of mass mm are attached gently to diametrically opposite points on the edge of the disc. What is the final angular velocity of the disc?

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Answer: (C) (MM+4 m)ω1\left(\frac{\mathrm{M}}{\mathrm{M}+4 \mathrm{~m}}\right) \omega_1

Angular momentum = conserved
12MR2ω1=2mR2ω+12MR2ω⇒ω=Mω1M+4 m\frac{1}{2} \mathrm{MR}^2 \omega_1=2 m R^2 \omega+\frac{1}{2} \mathrm{MR}^2 \omega \Rightarrow \omega=\frac{\mathrm{M} \omega_1}{\mathrm{M}+4 \mathrm{~m}}

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