A conducting sphere of density

floats in a liquid of density

and permittivity k. The sphere is submerged in the liquid to less than half its diameter . What charge must be imparted to the sphere so that it is half submerged into the liquid ? The radius of the sphere is equal to a.

hey i m not confident still i m trying

see the upthrust will be (₂-₁)g

and let s be charge density

total charge q=4x².s when half submerged to a distance x

this charge on sphere will induce a opp. charge on the molecules of water so i think i have cleared the doubt of karthik so there will be a electrostatic force in operation

now we have to integrate this to get charge on half sphere ,we get

                     (  ₂-₁)g=k.q/a²

now put value of q from above eqn i think u might get the ans

tell me if i m correct...

hey printing mistake it should be q² in the given formula rest i think is correct.