A cylindrical block of mass M and area of cross section A is floating in a liquid of density ρ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation i $s________.$
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Question

A cylindrical block of mass M and area of cross section A is floating in a liquid of density ρ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation i $s________.$

Options

G1 Physics · Accepted Answer

At equilibrium, let the immersed height be h. The buoyant force balances the weight: ρAhg = Mg. Now depress the cylinder downward by a small distance x. The extra displaced volume is Ax. Hence the additional upward buoyant force is ρAgx. This is the restoring force: F = -ρAgx. Therefore, Ma = -ρAgx. So, a = -(ρAg/M)x. Comparing with SHM, a = -ω²x, we get ω² = ρAg/M. Hence, ω = √(ρAg/M). Therefore, T = 2π/ω = 2π√[M/(ρAg)]. Correct option: A.

A cylindrical block of mass M and area of cross section A is floating in a liquid of density ρ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation i s________.