Physics - Rotation Question with Solution | TestHub

For rotational equilibrium of the sphere, it is necessary that vertical line (along which force Mg acts) through COM pass through contact point. This will ensure no torque about the contact point. Situation for maximum $\theta$ is shown in figure. Obviously, $\sin \theta =0.3$

If $\theta$ is less than ${\sin }^{-1}(0.3)$ the sphere can be rotated so that vertical line through COM passes through contact point. If $\theta$ is larger than ${\sin }^{-1}(0.3)$, the line of MG pass from right of contact point and will produce an unbalanced torque.