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Fluid Mechanics
Fluid Statics
GATE 2016
Hard

A frictionless, massless and leak-proof plug blocks a rectangular hole of dimensions 2R × L at the bottom of an open tank. The head of the plug has the shape of a semi-cylinder of radius R, submerged, with the tank filled with a liquid of density ρ up to the tip of the plug. Neglecting atmospheric pressure, the force F required to hold the plug in position is

  • A2ρR²gL(1 - π/4)
  • B2ρR²gL(1 + π/4)
  • CπR²ρgL
  • (π/2)ρR²gL

Explanation

The submerged semi-cylindrical plug head experiences a net upward hydrostatic (buoyant-type) force equal to the weight of liquid it displaces: F = ρg × Vsemicylinder = ρg × (πR²L)/2 = (π/2)ρR²gL. The holding force F must equal this upward push.

Source: GATE ME 2016 Set-2 (2016)

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