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

Options

A. `rhopigHR^(2)`
B. `pirhoHR^(2)`
C. `(4)/(3)pirhogHR^(2)`
D. `(2)/(3)pirhogHR^(2)`

Answer

D

Explanation

Buoyancy = force on base-force on slant surface `(f_(y))`
Force on slant surface = force on base-buoyancy
Force on slant surface `piR^(2)Hpg-(1)/(3)piR^(2)Hpg`
Force on slant surface `=(2)/(3)piR^(2)Hpg`