MCQ
A thin circular ring of mass $M$ and radius $R$ is rotating with a constant angular velocity $2 \; rads ^{-1}$ in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass $m$ be attached gently to the opposite ends of a diameter of ring, the ring will then rotate with an angular velocity (in $rads ^{-1}$ )
  • A
    $\frac{M}{(M+m)}$
  • B
    $\frac{( M +2 m )}{2 M }$
  • $\frac{2 M }{( M +2 m )}$
  • D
    $\frac{2( M +2 m )}{ M }$

Answer

Correct option: C.
$\frac{2 M }{( M +2 m )}$
c
Applying conservation of angular momentum

$M R^{2} \omega=\left(M R^{2}+2 m R^{2}\right) \omega^{\prime}$

$\omega^{\prime}=\frac{2 M }{ M +2 m }$

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