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A cone of radius $R$ and height $H$ , is hanging inside a liquid of density $ρ$ 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 atmospheric pressure)

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$ρ {πgHR}^{2}$

$\frac{4}{3} π ρ {gHR}^{2}$

$\frac{2}{3} π ρ {gHR}^{2}$

$π ρ {HR}^{2}$

answer is D.

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Detailed Solution

The buoyant force

$F_{b} = F_{b o t t o m} + F_{v e r t i c a l f o r c e o n s l i n t f o r c e}$

or $(\frac{π R^{2} H}{3}) ρ g = π R^{2} \times ρ g H + F_{v e r t i c a l f o r c e o n s l i n t f a c e}$

$\Rightarrow F_{v e r t i c a l f o r c e o n s l a n t f a c e} = - \frac{2}{3} π ρ g H R^{2}$ (downwards).

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