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Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions $2R \times L$ 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 $\rho$ 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

  1. $2\rho R^2gL(1-\dfrac{\pi }{4}) \\$
  2. $2\rho R^2gL(1+\dfrac{\pi }{4}) \\$
  3. $\pi R^2\rho gL \\$
  4. $\dfrac{\pi }{2}\rho R^2gL$
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