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

Question

Consider a frictionless, mass less and leak proof 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 semi-cylinder of radius R. The tank is filled with a liquid of density r 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$\rho$R²L$\left ( 1-\frac{\pi }{4} \right )$

      (b) 2$\rho$R²gL$\left ( 1+\frac{\pi }{4} \right )$

      (c) $\pi$R²rgL

      (d)$\frac{\pi }{2}\rho$R²rgL