Question

In a car lift, compressed air exerts a force $F_1$ on a small piston having a radius of $5.0\text{cm}$. This pressure is transmitted to the second piston of radius $10.0\text{cm}$. If the mass of the car to be lifted by the second piston is $1350\text{kg}$, calculate $F_1$ [Take $g=10{\text{m/s}}^2$]

• A. $1800\text{N}$
• B. $2400\text{N}$
• C. $3375\text{N}$
• D. $5625\text{N}$

Answer 1

The correct option is C $3375\text{N}$

Here, $r_1=\frac{5}{100}\text{m},r_2=\frac{10}{100}\text{m}$
$F_2=1350\times 10\text{N}$
As we know,
$\frac{F_1}{A_1}=\frac{F_2}{A_2}$
[From Pascal's law]
So, $F_1=\frac{A_1}{A_2}\times F_2$
i.e $F_1=\frac{\pi r_1^2}{\pi r_2^2}\times F_2=\frac{r_1^2}{r_2^2}\times F_2$
$\Rightarrow F_1=\frac{(5/100{)}^2}{(10/100{)}^2}\times 1350\times 10=3375\text{N}$