Physics Question from JEE Main 2025 · 4 April, Shift 2

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 $\frac{R}{2}$ is $x\omega_1$. The value of $x$ is _____.