Question

Find the height of obstacle so that the sphere can stay in equilibrium.

Answer 1

The sphere is on the verge of toppling when a line of action of weight passes through the edge. The equilibrium is because of the line of action of weight and the normal reaction provided by the edge.

So, $\cos \theta =\frac{R-h}{R}$

or, $h=R-R\cos \theta$