A vertical triangular plate ABC is placed inside water with side … - Vidyadip

MCQ

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 $\rho $ and atmospheric pressure $P_0$ )

A
$\left( {{P_0} + h\rho g} \right)\frac{1}{2}ab$
✓
$\left( {{P_0} + h\rho g} \right)\frac{1}{2}ab + \frac{{{a^2}b}}{3}\rho g$
C
$\left[ {{P_0} + \rho g\left( {h + a} \right)} \right]\frac{1}{2}ab$
D
$0$

✓

Answer

Correct option: B.

$\left( {{P_0} + h\rho g} \right)\frac{1}{2}ab + \frac{{{a^2}b}}{3}\rho g$

b
$\mathrm{F}=$ pressure at centroid $\times$ area

$\mathrm{F}=\left(\mathrm{P}_{0}+\frac{\mathrm{h}+\mathrm{h}+\mathrm{a}+\mathrm{h}+\mathrm{a}}{3} \rho \mathrm{g}\right) \frac{1}{2} \mathrm{ab}$

$=\left(P_{0}+\left(h+\frac{2 a}{3}\right) \rho g\right) \frac{1}{2} a b$

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