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