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A sphere is just immersed in a liquid. Find the ratio of hydro

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A sphere is just immersed in a liquid. Find the ratio of hydrostatic force acting on top and bottom half of the sphere.

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Text solutionVerified

F_{buoyant} = F_{0} - F_{s_{1}}

ρ γ g = Rg ρ \cdot π R^{2} - F_{s_{1}}

F_{s_{2}} = π R^{3} ρ g - ρ g γ = π R^{3} ρ g - ρ g \cdot \frac{2}{3} π R^{3}

F_{s_{1}} = π R^{3} ρ g (\frac{1}{3})

Similarly,

F_{b} = F_{s_{2}} - F_{0}

\Rightarrow F_{s_{2}} = F_{b} + F_{0} = ρ g \cdot \frac{2}{3} π R^{3} + π R^{3} ρ g

= \frac{5}{3} π R^{3} ρ g

\frac{F _{s_{2}}}{F _{s_{1}}} = \frac{5}{1}

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Question Text	A sphere is just immersed in a liquid. Find the ratio of hydrostatic force acting on top and bottom half of the sphere.
Topic	Mechanical Properties of Fluids
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	150