Question

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 depth $h$ below the liquid surface. The force on the bottom of the cylinder by the liquid is

• A. $M g$
• B. $M g-V \rho g$
• C. $M g+\pi R^{2} h \rho g$
• D. $\rho g\left(V+\pi R^{2} h\right)$

Answer 1

Answer: (D)

$ F_{2}=F_{1}+$ upthrust
or $ F_{2}=(\rho g h)\left(\pi R^{2}\right)+V \rho g$
or $ F_{2}=\rho g\left(\pi R^{2} h+V\right)$