Fluid Pressure !

A container has a hole in the bottom of a container. The hole is closed with a hemispherical cap of radius R R as shown in the figure. The vessel is filled with a liquid of density ρ \rho upto height H H from the bottom of the container. The force with which the cap presses the bottom of the vessel is :

ρ g π R 2 ( H 4 3 R ) \rho g\pi R^2 \bigg(H - \frac{4}{3} R \bigg) ρ g π R 2 ( H 2 3 R ) \rho g\pi R^2 \bigg(H - \frac{2}{3} R \bigg) ρ g π R 2 H \rho g\pi R^2H 2 3 ρ g R 3 \frac{2}{3}\rho gR^3

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