Determine the change in potential energy of a body when it is raised through a height h, inside water. Volume of the body is V, its density is `rho` and the density of water is `rho_(0)`. Given your answer for the situations when (i) `rhogtrho_(0)` and (ii) `rholtrho_(0)`.

Explanation

Two forces act on a body when it is immersed in water. One is its weight (acting downwards) and another is the buoyant force (acting upwards). Force due to weight = `Vrhog`, and upthrust due to buoyancy = `Vrho_(0)g`.
(i) If `rhogtrho_(0)`, the weight of the body becomes greater than the upthrust.
Hence, resultant downward force
`Vrhog-Vrho_(0)g=Vg(rho-rho_(0))`.
If the body is raised to a height h against this force, then work done = `Vg(rho-rho_(0))h` = increase in potential energy.
(ii) When `rhogtrho_(0)`, then upthrust becomes greater than the weight. Then resultant upward force = `Vg(rho_(0)-rho)`. To raise the body through a height h, work done = `Vg(rho_(0)-rho)h` = decrease in potential energy.