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A thin walled hemispherical shell of mass m and radius R is pressed against a smooth vertical wall. Through a very small aperture at its top, water of density $ρ$ is filled in it completely. Minimum magnitude of force is to be applied to the shell for liquid not to escape from it. Weight of hemispherical shell is mg and total mass of water is $M= \frac{2}{3} {πR}^{3} ρ$

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Horizontal component of net force $\frac{1}{2} π R^{3} ρ g$

Vertical component of force is $(M+m) g$

Net external force is $Mg \sqrt{\frac{9}{4} + {(1+ \frac{m}{M})}^{2}}$

Direction of net force is given by ${θ= tan}^{-1} \frac{(m+M)}{3M}$ , where $θ$ is from horizontal direction

answer is B, C.

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Detailed Solution

$F_{H} = (ρ g R) π R^{2} = ρ g π R^{3} = \frac{3 M g}{2} F v = (M + m) g F_{n e t} = \sqrt{{[(M + m) g]}^{2} + {(\frac{3 M g}{2})}^{2}} F_{n e t} = M g \sqrt{\frac{9}{4} {(1 + \frac{m}{M})}^{2}}$

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