Question

A cone of radius R and height H, is hanging inside a liquid of density 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. $\rho \pi H{R}^2$
• 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

The correct option is D

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

$Upthrust=F_{\left(basesurface\right)}-F_{\left(slantsurface\right)}{F}_{\left(slantsurface\right)}=F_{\left(basesurface\right)}–Upthrust=\left(\rho gH\right)\left(\pi R^2\right)-\left(\frac{1}{3}\pi R^{2}H\right)\rho g=\frac{2}{3}\pi gH{R}^2$