Q 11-06-260JEE MainJEE Main 2025 (4 Apr, Shift 2)Medium
A solid sphere with uniform density and radius $R$ is rotating initially with constant angular velocity $\omega_1$ about its diameter. After some time during the rotation it starts losing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius becomes $R/2$ is $x\omega_1$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 32
The density stays uniform, so $M \propto R^3$: at radius $R/2$ the mass is $M/8$.
With no external torque, angular momentum is conserved:
$$\tfrac25MR^2\omega_1 = \tfrac25\cdot\frac M8\cdot\frac{R^2}{4}\omega_2 \Rightarrow \omega_2 = 32\omega_1$$
So $x = 32$.
Solution by Sreeraj P, M.Sc Physics