Question

A downward force of $100\text{N}$ is applied to the small piston with a diameter of $50\text{cm}$ in the hydraulic lift system as shown in figure. What will be the upward force exerted on the large position with a diameter of $1\text{m}$?

• A. $300\text{N}$
• B. $50\text{N}$
• C. $400\text{N}$
• D. $600\text{N}$

Answer 1

The correct option is C $400\text{N}$


According to pascal's law, the change in pressure of a confined fluid is transmitted undiminished in all direction. Therefore,
$P_1=P_2$
$\therefore \frac{F_1}{A_1}=\frac{F_2}{A_2}...\left(i\right)$
Where $A_1$ and $A_2$ are the areas of piston.
$\Rightarrow F_2=F_1.\frac{A_2}{A_1}$
$F_2=100\times \frac{\pi r_2^2}{\pi r_1^2}$
$F_2=\frac{100\times r_2^2}{r_1^2}$
$\therefore F_2=100\times {\left(\frac{0.5}{0.25}\right)}^2=400\text{N}$