Question

A thin circular ring of mass M and radius R is rotating with a constant angular velocity of 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 the ring, the ring will then rotate with an angular velocity (in rads^-1).

Options

• `M/((M + m)`

• `((M + 2m))/(2M)`

• `(2M)/((M + 2m)`

• `(2(M + 2m))/M`

Answer 1

`underlinebb((2M)/((M + 2m))`

Explanation:

`L_i = MR^2omega_i`

`L_f = (M + 2m)R^2omega_f`

As no external torque acts on the system.

So, `vecL` = constant ⇒ `vecL_i = vecL_f`

⇒ `MR^2omega_i = (m + 2m)R^2omega_f ⇒ omega_f = M/(M + 2m)omega_i`

⇒ `omega_f = (2M)/(M + 2m)`