A block of rectangular size of mass m and area of cross-section A, floats in a liquid of density ρ. If we  give a small vertical displacement from equilibrium, it undergoes SHM with time period T, then  [AIIMS 2018]

For a rectangular block, floating in a liquid as shown in the figure below, thenAt equilibrium, mg = Vρg = Alρg⇒                      m=Aρlwhere, I = length of part immersed in liquid.When it is given in downward displacement y, restoring force (upward direction) on block is            F=-[A(l + y) ρg-mg]   =-[A(l+y) ρg-Alρg]=-Aρgyi.e. F∝-y or a∝-y, so it executes SHM.∴  Time period = 2πInertia factorSpring factor                         T=2πmAρg⇒T2∝mAρor                      T2∝1ρ