Question

A force of 50 kgf is applied to the smaller piston of area 20 cm² to balance a force of 2000 kgf on larger piston. Find the area of larger piston.

Answer 1

The area of the larger piston = 800 cm²

The hydraulic press is based on the principle of Pascal's law , which states that any pressure change in a liquid is uniformly distributed throughout the liquid.

Let ,

F1 = 50 Kgf = force on small piston

F2= 2000 Kgf = force on large piston

A1= 20 cm^2 = area of the small piston

A2 = area of the large piston

For the hydraulic machine -

Pressure on both pistons will be equal

P1 = P2 => F1/A1=F2/A2

=> A2=(F2×A1)/F1

=> A2=(2000×20)/50

=> A2= 800 cm²

The area of the larger piston = 800 cm²

Answer 2

Given :

A1=20

F1=50 kgf

F2=2000 kgf

To Find : A2=?

Solution :

We know that

$Pressure,P=\frac{F}{A}\\P_1=P_2\\\frac{F_1}{A_1}=\frac{F_2}{A_2}\\A_2=\frac{A_1}{F_1}\times F_2\\ A_2=\frac{20}{50}\times 2000\\A_2=800\ cm^2$

Therefore the larger area piston is :$800\ cm^{2}$