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A hemispherical light shell of radius R is filled with fluid of density $ρ$ and covered with a plate as in figure(a). Then whole system is inverted and a small hole is made at top as in figure(b). Minimum force that should be applied on shell to prevent any fluid to escape is $F = \frac{2}{x} ρ (π R^{3}) g$ , find $x$ : (The plate is placed on a horizontal floor)

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Detailed Solution

$F = \int_{0}^{π / 2} [σ g R (1 - C o s θ) \times 2 π R \sin θ \times R d θ \times C o s θ]$

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