JEE Main 2025 — Rotational Motion Question with Solution

A solid sphere with uniform density and radius $R$ is rotating initially with constant angular velocity $\left({\omega }_1\right)$ about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become $\mathrm{R}/2$ is $x{\omega }_1$. The value of $x$ is _________.