A hemispherical portion of radius R is removed from the bottom of a cylinder of radius R. The volume of the remaining cylinder is V and its mass is M. It suspended by a string in a liquid of density `rho` where it stays vertical. The upper surface of cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder bby the liquid is

Options

A. Mg
B. Mg - h `rho` g
C. `Mg + pi R^(2)h rho g`
D. `rho g(V+pi R^(2)h)`

Answer

D

Explanation

The net upward force on the bottom of cylinder = wt. of liquid displaced by cylinder + thrust on the upper surface of cylinder due to h column of lliquid. `V rho g+h rho gxxpi R^(2)`
`=rho g(V+pi R^(2)h)`