First slide

Pressure in a fluid-mechanical properties of fluids

Question

A heavy load W is supported on a platform of area S by applying a force F on a small piston of area $S / 10$ . The value of F for equilibrium is $(x < < H)$

Moderate

A

$\frac{W}{10}$
B

$\frac{W + ρ g H S}{10}$
C

$\frac{W - ρ g H S}{10}$
D

$10 W$

Solution

According to Pascal’s law the pressure at point P below the lower piston inside the liquid $= \frac{W}{S} + ρ g H$ $(x < < H)$
The pressure caused by the force ‘F’ is $= \frac{F}{(\frac{S}{10})} = \frac{10 F}{S}$
As the liquid is at equilibrium $\frac{W}{S} + ρ g H = \frac{10 F}{S}$
$\Rightarrow 10 F = W + ρ g H S$
$∴ F = \frac{W + ρ g H S}{10}$
Therefore, the correct answer is (B)

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