Question

A cube of side $a$ is placed on an inclined plane of inclination $\theta$. What is the maximum value of $\theta$ in degrees for which the cube will not topple?

Answer 1

The cube will not topple until the line of action of CM passes through the point A of the cube because in that case the net torque around the point A will be zero.
That is, $\tan \theta =\frac{AX}{OX}=\frac{a/2}{a/2}$ or $\theta ={45}^{\circ }$