Rotation 2 Question 14
14. A thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega$. Two objects, each of mass $m$, are attached gently to the opposite ends of a diameter of the ring. The wheel now rotates with an angular velocity
(1983, 1M)
(a) $\omega M /(M+m)$
(b) $\omega(M-2 m) /(M+2 m)$
(c) $\omega M /(M+2 m)$
(d) $\omega(M+2 m) / M$
Objective Question II (One or more correct option)
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Answer:
Correct Answer: 14. (c)
Solution:
- $I _1 \omega _1=I _2 \omega _2$
$$ \begin{aligned} \therefore \omega _2 & =\frac{I _1}{I _2} \omega=\frac{M r^{2}}{M r^{2}+2 m r^{2}} \omega \\ & =\frac{M}{M+2 m} \omega \end{aligned} $$
