Discussion
If\(F_{1}\) is the force exerted by air on a small piston of area of cross-section \(A_{1}\) in a car lift , then the force\(F_{2}\) realised on the second piston of area of cross-section \(A_{2}\)due to the transfer of pressure is
Answer: B
\(F_{2} = F_{1}\frac{A_{2}}{A_{1}}\).
By Pascal's law, the pressure applied at the small piston is transmitted undiminished through the fluid to the large piston:
\[ \begin{aligned} \frac{F_{1}}{A_{1}} &= \frac{F_{2}}{A_{2}} \\ F_{2} &= F_{1}\frac{A_{2}}{A_{1}} \end{aligned} \]
Because \(A_{2} \gt A_{1}\), the output force is larger, which is why a hydraulic lift can raise a car. \(F_{1}\frac{A_{1}}{A_{2}}\) inverts the ratio and would make the lift reduce the force. The square-root forms have no basis in Pascal's law, and the last option is not even a force.
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