Question

A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rad s-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 rad s-1)

• A. $\frac{M}{M+m}$
• B. $\frac{M+2m}{2M}$
• C. $\frac{2M}{M+2m}$
• D. $\frac{2(M+2m)}{M}$

Answer 1

Answer: (C)

$\frac{2M}{M+2m}$

Answer 2

$l_1 \omega_1 = l_2 \omega_2$
$⇒$ $MR^2 \times2 = (MR^2 + 2mR^2) \omega^2$
$⇒$ $\omega_2 = \frac{2M}{M+2m}$
So,the correct option is C: $\frac{2M}{M+2m}$