Question

A car of mass $500kg$ is lifted by a hydraulic jack that consist of two pistons. If the diameter of large and small pistons are $2m$ and $20cm$ respectively, then force required to lift the car by smaller piston is (take, $g=10m/s^2$ )

• A. $5000N$
• B. $25N$
• C. $500N$
• D. $50N$

Answer 1

Answer: (D)

Given, mass of car $=500kg$
Weight of car, $w=mg=500\times 10$
$=5\times 10^{3}N$,
$d_1=2m$
$\Rightarrow r_1=1m,d_2=20cm$
$\Rightarrow r_2=10cm=0.1m$
According to Pascal's law,
$\frac{F_2}{A_2}=\frac{F_1}{A_1}$
$\Rightarrow \frac{F_2}{\pi r_2^2}=\frac{w}{\pi r_1^2}$
$\Rightarrow F_2=w{\left(\frac{r_2}{r_1}\right)}^2$
$=5\times 10^3{\left(\frac{0.1}{1}\right)}^2=50N$