A brass cube of side a and density σ is floating in mercury of density ρ. If the cube is displaced a bit vertically, it executes S.H.M. Its time period will be

As a is the side of cube σ is its density.Mass of cube is a2 σ its weight = a3σgLet h be the height of cube immersed in liquid of density ρ in equilibrium then, F = a2hρg = Mg = a3σgIf it is pushed down by y then the buoyant forceF' = a2(h+y)ρgRestoring force is ∆F = F'-F = a2(h+y)σg-a2hσg                           = a2yρgRestoring acceleration = ∆FM = -a2yρgM = -a2ρga2σyMotion is S.H.M.⇒T =2πa3σa2ρg = 2πaσρg