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Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions 2R × L at the bottom of an open tank as shown in the figure. The head of the plug has the shape of a semi-cylinder of radius R. The tank is filled with a liquid of density ρ up to the tip of the plug. The gravitational acceleration is g. Neglect the effect of the atmospheric pressure.

1. 2ρR²gL (1 − π/4)
2. 2ρR²gL (1 + π/4)
3. πR²ρgL
4. (π/2) ρR²gL

Correct answer: 2ρR²gL (1 − π/4)

Solution

The correct option accounts for the pressure exerted by the liquid on the plug, which is influenced by both the rectangular area and the semi-circular shape of the plug. The term (1 − π/4) arises from the geometry of the semi-cylinder, reflecting the effective area that contributes to the force on the plug, leading to the correct calculation of the hydrostatic pressure.

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