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 θ and is left. The restoring force acting on it is

Step-by-step solution

Let l be the length of the cylinder in water it is in the vertical position and A be the cross-sectional area of the cylinder. As cylinder is floating so Weight of cylinder = upward thrust m g = A l ρ g or m = A l ρ When the cylinder is tilled through an angle θ , length of cylinder in water = l cos ⁡ θ Weight of water displaced = l cos ⁡ θ A ρ g Restoring force = l A ρ g cos ⁡ θ = l A ρ g = l A ρ g 1 cos ⁡ θ - 1 = m g 1 cos ⁡ θ - 1