A hemispherical container of mass M is placed upside down on a smooth horizontal surface. Through a small hole at the top of container, water is poured into it as shown in the figure. Exactly when the

Question

A hemispherical container of mass M is placed upside down on a smooth horizontal surface. Through a small hole at the top of container, water is poured into it as shown in the figure. Exactly when the container gets fill (completely filled), water starts leaking from between the table and the edge of the container. The density of water is ρ and radius of hemi-spherical container is R . (Neglect the atmospheric pressure and effect of surface tension) choose the correct statement(s).:

TestHub · Accepted Answer

Half filled (water up to z = R /2 ): upward force on the wetted wall F = ∫ ρ g ( 2 R ​ − z ) R z ​ d A = 24 1 ​ π R 3 ρ g - (A) correct, (B) incorrect When just full, leaking starts: normal reaction from the table becomes zero, so F B ​ = M g Full upward force: F B ​ = ρ g [ π R 3 − 3 2 ​ π R 3 ] = 3 1 ​ π R 3 ρ g M = 3 π R 3 ρ ​ - (D) correct, (C) incorrect

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