Question

A thin circular ring of '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 the diameter of the ring. The wheel now rotates with an angular velocity.

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

Answer 1

The correct option is C $\frac{M\omega }{(M+2m)}$

Let I be MOI of ring initially and w be its angular velocity

Let them change to I' and w'

$I=m{R}^{2}I=M{R}^2+2m{R}^2=(M+2m)R^2{L}_i=I\omega angularmomentumisconserved\therefore I\omega =I^{\prime }{\omega }^{\prime }\Rightarrow {\omega }^{\prime }=\frac{I}{I^{\prime }}\omega =\frac{M}{(M+2m)}\omega$