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A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity ?. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity:
Options
(a) ?M / M + 2m
(b) ? (M + 2m) / M
(c) ?M / M + m
(d) ? (M – 2m) / M + 2m
Correct Answer:
?M / M + 2m
Explanation:
In abstance of external torque, L = I? = constant
I₁?￢ﾂﾁ = I₂?￢ﾂﾂ,I₁ = MR²,I₂ = MR² + 2mR²
(Moment of inertia of a thin ciruclar ring about axis vertical to its plane = MR²)
?￢ﾂﾂ = I₁ / I₂ ⇒ ? = ?M / M + 2m
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Topics: Motion of system of Particles and Rigid Body
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Subject: Physics
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