Answer :

Here we apply the concept of buoyant force


Let the wood part of the height of the wood be immersed into the water


Here the wood log experiences a buoyant force which is given as,


,


where ρ =density of wood log, V=volume of the water displaced by wood now at equilibrium, the buoyant force is balanced by the weight, i.e.,



------(1)


Now let the wood be displaced by depth into the water,


the volume of the water displaced by the wood is,


the buoyant force


there acts net restoring force on the wood log,



Putting equation (1) in the above we get,


-------(2)


is proportional to


wood performs a simple harmonic motion


Now the in S.H.M., we have


Comparing this equation with equation (2) we get,



For S.H.M, Time period


Substituting the value of k, we get,



Hence proved.


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