Probability — practice question

A uniform solid hemisphere, with weight $60\text{ N}$ and radius $0.8\text{ m}$, is in limiting equilibrium on a rough horizontal plane with its curved face in contact with the plane. The hemisphere’s axis of symmetry makes an angle $\theta$ with the horizontal, where $\cos\theta = 0.28$. A horizontal force of magnitude $P\text{ N}$ is applied at the lowest point of the circular rim to keep the hemisphere in equilibrium (see diagram).