Physics Question 50 – JEE-MAIN 2025

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 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 _______.