A thin circular ring of mass M and radius R rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity ω . Four small spheres each of mass m (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be

Question

A thin circular ring of mass M and radius R rotates about an axis through its centre and perpendicular to its plane, with a constant angular velocity ω . Four small spheres each of mass m (negligible radius) are kept gently to the opposite ends of two mutually perpendicular diameters of the ring. The new angular velocity of the ring will be, M 4 m ω, M + 4 m M ω, M M - 4 m ω, M M + 4 m ω

MARKS App · Accepted Answer

According to conservation of angular momentum, Iω = constant, hence we can write I 1 ω 1 = I 2 ω 2 or MR 2 ω = M + 4 m R 2 ω 2 or ω 2 = M M + 4 m ω

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