A small cork of density is tied to a light string of length l . The other end of the string is anchored to the bottom of a tank filled with a non-viscous liquid of density (where > ). The cork is completely submerged and is allowed to oscillate slightly in the liquid. The time period of its simple harmonic motion will be

Step-by-step solution

For the submerged cork, the buoyant force acts upwards and its weight acts downwards. Since > , the buoyant force is greater than the weight, keeping the string taut vertically upwards (an inverted pendulum). Let the volume of the cork be V . Buoyant force, F_B = V g (upwards) Weight of the cork, W = V g (downwards) Net upward force at equilibrium, F_ net = F_B - W = V g - V g = V( - )g This net force provides the effective "weight" that acts as the restoring force when the cork is displaced by a small angle . Effe