Since no external torque acts on the solid sphere as it cools and shrinks, its angular momentum ($L$) remains conserved. According to the law of conservation of angular momentum, $L = I\omega = \text{constant}$ .

The initial moment of inertia of the solid sphere is $I_1 = \frac{2}{5}MR^2$, and its initial angular velocity is $\omega_1 = \omega$.

When the radius reduces to $R_2 = \frac{R}{n}$, the new moment of inertia becomes: $I_2 = \frac{2}{5}M\left(\frac{R}{n}\right)^2 = \frac{1}{n^2}\left(\frac{2}{5}MR^2\right) = \frac{I_1}{n^2}$

Applying the conservation of angular momentum: $I_1\omega_1 = I_2\omega_2$ $I_1\omega = \left(\frac{I_1}{n^2}\right)\omega_2$ $\omega_2 = n^2\omega$

Thus, its new angular velocity becomes $n^2\omega$.