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

Answer

D

Explanation

According to Archimedes’ principle, upthrust = weight of the fluid displaced, `F_("bottom")-F_("top")=Vrhog`
`therefore" "F_("bottom")=F_("top")+Vrhog`
`=P_(1)xxA+Vrhog`
`=(hrhog)xx(piR^2)+Vrhog=rhog[piR^(2)h+V]`