Question

A piston of cross-sectional area $100{\text{cm}}^2$ is used in a hydraulic pump to exert a force of ${10}^7\text{dyne}$ on the water. The cross-sectional area of the other piston which supports a truck of mass $2000\text{kg}$ is

• A. $9.8\times {10}^2{\text{cm}}^2$
• B. $9.8\times {10}^3{\text{cm}}^2$
• C. $1.96\times {10}^3{\text{cm}}^2$
• D. $1.96\times {10}^4{\text{cm}}^2$

Answer 1

The correct option is D $1.96\times {10}^4{\text{cm}}^2$

As we know,
$\frac{F_1}{A_1}=\frac{F_2}{A_2}$
[From Pascal's law, pressure change at one piston is transmitted to the other piston]
$\therefore A_2=\frac{F_2}{F_1}\times A_1$
Here, $F_1={10}^7\text{dyne}=100\text{N}$
[$\because 1\text{N}={10}^5\text{dyne}$]
and $F_2=2000\times g\text{N}$
$A_1=100{\text{cm}}^2$

$\Rightarrow A_2=\left(\frac{2000\times 9.8}{{10}^2}\right)\left(100\right)$
$\Rightarrow A_2=1.96\times {10}^4{\text{cm}}^2$