A rectangular block of mass 'm' and cross-sectional area 'A' floats on a liquid of density ' '. It is given a small vertical displacement from equilibrium, it starts oscillating with frequency (g=acceleration due to gravity)

Step-by-step solution

Let the block be displaced downwards by a small distance x from its equilibrium position. The additional volume submerged in the liquid is Ax . The extra buoyant force acting upwards provides the restoring force, which is given by F = -( additional volume ) g F = -A x g Comparing this with the standard equation of simple harmonic motion F = -kx , we get the effective force constant k = A g . The angular frequency of oscillation is = k m = A g m . The frequency of oscillation is f = 2 = 1 2 A g m . Answer: 1 2 A g m