JEE Advanced 2025 · Paper 2, Physics question 9

Magnetic moment. On a conductor the charge sits on the surface, so this is a rotating charged shell. A ring at polar angle $\theta$ carries charge $dq=\frac Q2\sin\theta\,d\theta$ and has moment $dq\frac\omega{2\pi}\pi R^2\sin^2\theta$. Integrating:
$$\mu=\frac{Q\omega R^2}{3}.$$

Angular momentum. The mass is uniform in the solid sphere: $L=\frac25MR^2\omega$.

Ratio.
$$\frac\mu L=\frac{5Q}{6M}=\frac53\cdot\frac{Q}{2M},\qquad\alpha=\frac53\approx1.67.$$