Q. A solid sphere is rotating about a diameter at an angular velocity $\omega$. If it cools so that its radius reduces to $\frac{1}{n}$ of its original value, its angular velocity becomes
A) $\frac{\omega}{n}$
B) $\frac{\omega}{n^{2}}$
C) $n\omega$
D) $n^{2}\omega$
Explanation
(d) On applying law of conservation of angular momentum
$I_{1}\omega_{1} = I_{2}\omega_{2}$
For solid sphere,
$I = \frac{2}{5}mr^{2} \Rightarrow \frac{2}{5}mr_{1}^{2}\omega_{1} = \frac{2}{5}mr_{2}^{2}\omega_{2}$
$r^{2}\omega = \left( \frac{r}{n} \right)^{2}\omega_{2} \Rightarrow \omega_{2} = n^{2}\omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.