Consider a frictionless, massless and leak-proof plug blocking

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 ρup 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

Total volume ⇒ V_total = 2R × L × R = 2 R²L ...(i)

Volume : V₁ =	πR₂	× L....(ii)
	2

F = Weight of fluit =
[V_total – V₁] ρg

=		2R²L -	πR²L		ρg
			2

F = 2GρR²gL		1 -	π
			4

2ρR²gL		1 -	π
			4

2₀R²gL		1 +	π
			4