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 R$/2.$ What is the final angular speed of the sphere?

Hint: For moment of inertia of sphere $(),$ use r $=$ R to find its initial angular momentum, and use r $=$ R$/2$ to find its final angular momentum. Then use conservation of angular momentum.

A$.$

w

B$.$

w $/2$

C$.$

$2$ w

D$.$

$4$ w