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A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity $ω$ . Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity $ω$ ' is

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$\frac{ωm}{(m + M)}$

$\frac{ω (m - 2 M)}{(m + 2 M)}$

$\frac{ω (m + 2 M)}{m}$

$\frac{ωm}{(m + 2 M)}$

answer is C.

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Detailed Solution

From conservation of angular momentum

${mr}^{2} ω = (m + 2 M) r^{2} ω'$

$ω' = \frac{mω}{m + 2 M}$

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