Question

A hydraulic lift has two pistons, the larger cross-sectional area is 40 times the smaller cross-sectional area. If an input force of 25 N is applied on the smaller cross-section, then the output force is

• A. 100 N
• B. 1000 N
• C. 2000 N
• D. 1500 N

Answer 1

The correct option is B

1000 N

Given, input force on the smaller cross-section $=25$ N and Area of larger cross-section $=40\times \text{Area of smaller cross section}$ or $\frac{\text{Area of larger cross-section}}{\text{Area of smaller cross section}}=40$

According to Pascal's law,

$\frac{\text{Input force on the smaller cross-section}}{\text{Area of smaller cross section}}=\frac{\text{Output force on larger cross-section}}{\text{Area of larger cross-section}}$

$\Rightarrow \frac{\text{Input force on the smaller cross-section}}{\text{Output force on larger cross-section}}=\frac{\text{Area of smaller cross section}}{\text{Area of larger cross-section}}$

$\Rightarrow \frac{25}{\text{Output force on larger cross-section}}=\frac{1}{40}$

On solving we get, Output force on larger cross-section = 1000 N