Hydraulic Pressure And Pascal's Law

NCERT Class 11, Chapter 10 (Mechanical Properties of Fluids) presents Pascal's law, which states that pressure applied to an enclosed incompressible fluid is transmitted undiminished to every point. In a hydraulic lift the pressure under both pistons is equal, so $\frac{F_1}{A_1}=\frac{F_2}{A_2}$. Rearranging for the small-piston force: $F_1=F_2\times \frac{A_1}{A_2}$. Substituting $F_2=20000\text{N}$, $A_1=0.01{\text{m}}^2$ and $A_2=0.5{\text{m}}^2$ gives $F_1=20000\times \frac{0.01}{0.5}=20000\times 0.02=400\text{N}$. The option 800 N wrongly doubles the area ratio. The option 200 N halves the correct value through an arithmetic slip. The option 1000 N uses an inverted ratio. The essential idea is that pressure, not force, is the same on both sides, so the force scales directly with the piston area; the larger piston experiences a proportionally larger force. As a magnitude check, the small piston force of 400 N is fifty times smaller than the supported weight of 20000 N, exactly matching the fifty-to-one area ratio, which is the force multiplication that makes hydraulic lifts and car brakes so useful. The trade-off, by conservation of energy, is that the small piston must move fifty times farther than the large one.