Pascal's Law And Hydraulics

A hydraulic lift relies on Pascal's law, which states that a pressure applied to an enclosed incompressible fluid is transmitted undiminished to every part of the fluid and the container walls. Because the pressure is the same on both pistons, $\frac{F_1}{A_1}=\frac{F_2}{A_2}$, so a small force on the narrow piston balances a large force on the wide one. Solving for the input force, $F_1=F_2\frac{A_1}{A_2}=10000\times \frac{5}{250}=10000\times \frac{1}{50}=200\text{N}$. The value 100 N would require an area ratio of 1:100. The value 400 N doubles the correct force. The value 500 N uses an incorrect ratio of 1:20. This is the standard NCERT application of Pascal's law that explains the force-multiplying action of hydraulic machines. As a check, the area ratio of 50 means the device multiplies force fifty-fold, so lifting a 10000 N car with only 200 N input is exactly the expected mechanical advantage.