Working of hydraulic lift and hydraulic brakes is based on

The correct option is Pascal’s law.

Explanation and Principle:

1. Understanding Pascal's Law:
Pascal's law states that any pressure applied to an enclosed, incompressible fluid is transmitted equally and undiminished to every portion of the fluid and to the walls of its containing vessel.

Mathematically, if a force $F_1$ is applied on a piston of small cross-sectional area $A_1$, the pressure exerted on the fluid is:

$P=\frac{F_1}{A_1}$

According to Pascal's law, this same pressure $P$ is transmitted throughout the liquid to a larger piston of area $A_2$, producing a larger output force $F_2$:

$P=\frac{F_2}{A_2}$

Equating the two expressions for pressure:

$\frac{F_1}{A_1}=\frac{F_2}{A_2}\Rightarrow F_2=F_1\times \left(\frac{A_2}{A_1}\right)$

Since $A_2>A_1$, the output force $F_2$ is significantly greater than the input force $F_1$. This force-multiplying effect is the fundamental working principle behind both hydraulic lifts and hydraulic brakes.

2. Overview of Other Laws:
• Faraday's law: Relates to electromagnetic induction.
• Gay-Lussac’s law: Describes the relationship between the pressure and absolute temperature of a gas at constant volume.
• Coulomb's law: Calculates the electrostatic force between two electrical charges.

Therefore, the working of hydraulic lifts and hydraulic brakes is based on Pascal’s law.