In a car lift , compressed air exerts a force F , on a small piston having a radius of 5 cm . This pressure is transmitted to a second piston of radius 15 cm . The mass of the car to be lifted in 1350 Kg . Find F and the pressure necessary to accomplish this task is ,

Given that in a car lift

Force on pump plunger = F

${\text{r}}_{\text{1}}=5\text{cm}$

${\text{A}}_{\text{1}}=\pi 25\times {10}^{-4}{\text{m}}^2$

Weight on press plunger

$\text{W}=1350\text{kgf}$

${\text{A}}_{\text{2}}=\pi \times 225\times {10}^{-4}{\text{m}}^{\text{2}}$

We have $\frac{\text{F}}{{\text{A}}_1}\text{=}\frac{\text{W}}{{\text{A}}_2}$

$\Rightarrow \text{F}={\text{r}}^{\text{2}}\text{×}\frac{\text{W}}{{\text{R}}^{\text{2}}}={\left(5\times {10}^{-2}\right)}^2\times \frac{1350}{{\left(15\times {10}^{-2}\right)}^2}$

$\text{F}=\frac{25\times 13500}{225}\text{N}$

$\text{F}=1.5\times {10}^3\text{N}$

$\text{Pressure}=\frac{1500}{\pi \times 25\times {10}^{-4}}\text{or}\frac{6\times {10}^5}{3.14}$                                        

$=1.9\times {10}^5\text{Pa}$