A vertical triangular plate ABC is placed inside water with side BC parallel to water surface as shown. The force on one surface of plate by water is (density of water is $ρ$ and atmospheric pressure $P_{0}$ ) :-

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TestHub · Accepted Answer

Pressure at the triangular plate centroid times its area gives the force:
$\overset{ˉ}{h} = h + \frac{2 a}{3}$
$A = \frac{ab}{2}$
$F = (P_{0} + ρ g \overset{ˉ}{h}) A$
$F = (P_{0} + ρ g (h + \frac{2 a}{3})) \frac{ab}{2}$
$F = (P_{0} + h ρ g) \frac{ab}{2} + \frac{a ^{2} b ρ g}{3}$
Option B.

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