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 `omega=`

Options

A. `((M+2m)omega)/(2m)`
B. `(2Momega)/(M+2m)`
C. `((M+2m)omega)/M `
D. ` (Momega)/(M+2m)`

Answer

D

Explanation

In the absence of external torque , angular momentum remain constant
` L = I_(omega) = I^(1)omega^(1) :. MR^(2)omega = (M+2m) R^(2)omega^(1)`
` rArr omega^(1) = (Momega)/((M+2m))`