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.The force F required to hold the plug in its position is

\(2\rho {R^2}gL\left( {1 + \frac{\pi }{4}} \right)\)

\(2\rho {R^2}gL\left( {1 - \frac{\pi }{4}} \right)\)

Consider a frictionless, massless and leak-proof plug blocking a recta

1.	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.The force F required to hold the plug in its position is
A.	\(2\rho {R^2}gL\left( {1 - \frac{\pi }{4}} \right)\)
B.	\(2\rho {R^2}gL\left( {1 + \frac{\pi }{4}} \right)\)
C.	πR2ρgL
D.	\(\frac{\pi }{2}\rho {R^2}gL\)
Answer» B. \(2\rho {R^2}gL\left( {1 + \frac{\pi }{4}} \right)\)

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