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 M. It is suspended by a string in a liquid of density `rho` where it stays vertical. The upper surface of the cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder by the liquid is

Options

A. Mg
B. Mg-Vdg
C. `Mg+piR^(2)hdg`
D. `dg(V+piR^(2)h)`

Answer

D

Explanation

The net upward force on the bottom of cylinder = Weight of liquid displaced by cylinder `+` thrust on the upper surface of cylinder to h column of liquid .
`=Vdg+hdgxxpiR^(2)`
`=dg(V+piR^(2)h)`