Question

A cone of radius R and height H, is hanging inside a liquid of density $\rho$ by means of a string as shown in the figure . The force, due to the liquid acting on the slant surface of the cone is (Neglect atmosphere pressure)

• A. $\rho \pi gH{R}^2$
• B. $\pi \rho H{R}^2$
• C. $\frac{4}{3}\pi \rho gH{R}^2$
• D. $\frac{2}{3}\pi \rho gH{R}^2$

Answer 1

Upthrust = $F_{\text{(base surface)}}–F_{\text{(slant surface)}}$

$F_{\text{(slant surface)}}=F_{\text{(base surface)}}$ – Upthrust

$=\left(\rho gH\right)\left(\pi R^2\right)-\left(\frac{1}{3}\pi R^{2}H\right)\rho g$

$=\frac{2}{3}\pi \rho gH{R}^2$