Question

A uniformly tapering vessel of height $h$ whose lower and upper radii are $r$ and $R$ is completely filled with a liquid of density $\rho$. The force that acts on the base of the vessel due to the liquid is

• A. $\pi R^{2} h \rho g$
• B. $\pi r^{2} h \rho g$
• C. $\pi\left(\frac{R+r}{2}\right)^{2} h \rho g$
• D. $\frac{1}{3} \pi\left(R^{2}-r^{2}\right) h \rho g$

Answer 1

Answer: (B)

$P$ at base $=\rho g h$
$F_{\text {Base }}=P_{\text {Base }} \times A_{\text {Base }}=\rho g h \times \pi r^{2}=\pi r^{2} \rho g h$