JEE MAIN - Physics (2022 - 26th June Morning Shift - No. 5)
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).
$${M \over {(M + m)}}$$
$${{(M + 2m)} \over {2M}}$$
$${{2M} \over {(M + 2m)}}$$
$${{2(M + 2m)} \over M}$$
Explanation
$${I_1}{\omega _1} = {I_2}{\omega _2}$$
$$M{R^2}{\omega _1} = (M{R^2} + 2m{R^2}){\omega _2}$$
$${\omega _2} = \left( {{M \over {M + 2m}}} \right){\omega _1}$$
$${\omega _2} = 2\left( {{M \over {M + 2m}}} \right)$$
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