A solid sphere with uniform density and radius R is rotating initially with constant angular velocity (ω_1) about its diameter. After some time…

A solid sphere with uniform density and radius $\displaystyle R$ is rotating initially with constant angular velocity $\displaystyle \left(\omega_1\right)$ 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 $\displaystyle \mathrm{R} / 2$ is $\displaystyle x \omega_1$. The value of $\displaystyle x$ is $\displaystyle \_\_\_\_$.