A hollow cylinder of mass m made heavy at its bottom is floating vertically in water. It is tilted from its vertical position through an angle $\mathrm{\theta }$ and is left. The respecting force acting on it is

Let l be the length of the cylinder, when vertical, in water. Let A be the cross-sectional area of the cylinder. Equating weight of the cylinder with the upthrust, we get

           Mg = $\mathrm{Al\rho g} \mathrm{or} \mathrm{m} = \mathrm{Al\rho }$

When the cylinder is titled through an angle $\mathrm{\theta }, \mathrm{length}$ of cyliner in water = $\frac{\mathrm{l}}{\cos \mathrm{\theta }}$

Weight of water displaced = $\frac{\mathrm{l}}{\cos \mathrm{\theta }}\mathrm{A\rho g}$

Restoring force = $\frac{\mathrm{lA\rho g}}{\mathrm{cos\theta }}-\mathrm{lA\rho g}$

                          = $\mathrm{lA\rho g}[\frac{1}{\mathrm{cos\theta }}-1] = \mathrm{mg}[\frac{1}{\mathrm{cos\theta }}-1]$