Question

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

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

Answer 1

Answer: (D)

Given, mass of car $=500\, kg$
Weight of car, $w=m g=500 \times 10$
$=5 \times 10^{3} \, N$,
$ d_{1}=2 m $
$\Rightarrow r_{1}=1 \, m , d_{2}=20\, cm$
$\Rightarrow r_{2}=10 \, cm =0.1 \, m$
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}} $
$\Rightarrow F_{2}=w\left(\frac{r_{2}}{r_{1}}\right)^{2}$
$=5 \times 10^{3}\left(\frac{0.1}{1}\right)^{2}=50\, N$