JEE Main 2025 — 4 April, Evening Shift — Question 64

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 $R / 2$ is $x \omega_{1}$. The value of $x$ is $\qquad$ -.