QUESTION $26$

A solid sphere of radius $R$ rotates about a diameter with an angular speed $w.$ The sphere then collapses under the action of internal forces to a final radius $\frac{R}{2}.$ What is the final angular speed of the sphere?

Hint: For moment of inertia of sphere $(I=\frac{2}{5}M{r}^2),$ use $r=R$ to find its initial angular momentum, and use $r=\frac{R}{2}$ to find its final angular momentum. Then use conservation of angular momentum.

A$.2$ w

B$.4$ w

C$.$ w

D$.$w$/2$