Some liquid is filled in a cylindrical vessel of radius $R$ . Let $F_{1}$ be the force applied by the liquid on the bottom of the cylinder. Now the same liquid is poured into the vessel of uniform square cross section of side $R$ . Let $F_{2}$ be the force applied by the liquid on the bottom of this new vessel. (Neglect atmosphere pressure) Then

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$F_{1} = F_{2}$

$F_{1} = \frac{F_{2}}{π}$

$F_{1} = π F_{2}$

$F_{1} = \sqrt{π} F_{2}$

answer is D.

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Detailed Solution

$π R^{2} h_{1} = R^{2} h_{2}$

$∴ π h_{1} = h_{2}$

$\frac{F_{1}}{F_{2}} = \frac{ρ g h_{1} x π R^{2}}{ρ g h_{2} x R^{2}} = \frac{π h_{1}}{h_{2}} = 1$

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