A spherical ball of radius r and relative density 0.5 is floating in equilibrium in water with half of it immersed in water. The work done in pushing the ball down so that whole of it is Just immersed in water is

When the ball is pushed down, the water gains P.E whereas the ball losses P.E. Hence gain in P.E. of water =Vρrg−V2ρ38rg =1312πr4ρg ∵V=43πr3  Loss in P.E. of ball =Vρ′rg =43πr4ρ′g  Work done =1312πr4ρg−4π3r4ρ′g =πr4ρg1312−43ρ′ρ =πr4ρg1312−43×0⋅5 =512πr4ρg