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  • A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity . Two objects each

A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity \omega. Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by

Option: 1

\frac{\left ( \text{M}+2\text{m} \right )\omega}{2\text{m}}


Option: 2

\frac{2\text{m}\omega}{\text{M}+2\text{m}}


Option: 3

\frac{\left ( \text{M}+2\text{m} \right )\omega}{\text{M}}


Option: 4

\frac{\text{M}\omega}{\text{M}+2\text{m}}


Answers (1)

best_answer

Moments of inertia (MOI) of the ring before attaching the masses I= MR2, 

MOI of the ring after attaching the masses I′=(M+2m)R2

Let angular momentum after the attaching the masses ω′

Since there is no external torque,  so we use conservation of angular momentum.

I×ω=I′×ω′

⇒MR2×ω=? \frac{MR^2 \times \omega'}{M+2m}

⇒ω′=? \frac{\omega M}{M+2m}

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