A liquid is filled in a cylindrical vessel of radius R. Let F₁ be the force exerted on the bottom. The same liquid is then poured into a vessel of uniform square cross-section of side R, and F₂ is the force on its bottom. Neglect atmospheric pressure. Which relation is correct?
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Question

A liquid is filled in a cylindrical vessel of radius R. Let F₁ be the force exerted on the bottom. The same liquid is then poured into a vessel of uniform square cross-section of side R, and F₂ is the force on its bottom. Neglect atmospheric pressure. Which relation is correct?

Options

G1 Physics · Accepted Answer

Step 1: The same liquid volume is transferred. If the initial cylinder height is h, πR²h = R²h′, hence h′ = πh. Step 2: Bottom force F = ρghA. Thus F₁ = ρgh·πR² and F₂ = ρg(πh)R², so F₁ = F₂. Final answer: D.