Question

The mechanical advantage of a hydraulic press is 10. A car of mass 1000 kg is lifted by it when placed on a piston of a hydraulic press of area of cross section $10c{m}^2$. What is the area of cross section of the piston where the effort applied ?

• A. $1c{m}^2$
• B. $2c{m}^2$
• C. $3c{m}^2$
• D. $4c{m}^2$

Answer 1

The correct option is A

$1c{m}^2$

Given:

$$\begin{gathered} \mathrm{mechanical}\mathrm{advantage}\mathrm{of}\mathrm{a}\mathrm{hydraulic}\mathrm{pressmechanical}\mathrm{advantage}\mathrm{of}\mathrm{a}\mathrm{hydraulic}\mathrm{press}=10 \\ \mathrm{Mass}\mathrm{of}\mathrm{car}\mathrm{on}\mathrm{piston}\mathrm{of}\mathrm{hydraulic}\mathrm{press}=1000\mathrm{kg} \\ \mathrm{Area}\mathrm{of}\mathrm{cross}\mathrm{section}\mathrm{of}\mathrm{hydraulic}\mathrm{press}=10{\mathrm{cm}}^2 \\ \mathrm{to}\mathrm{find}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{cross}\mathrm{section}\mathrm{of}\mathrm{piston}\mathrm{where}\mathrm{effort}\mathrm{is}\mathrm{applied} \\ \mathrm{we}\mathrm{know}\mathrm{that}\mathrm{mechanical}\mathrm{advantage}=\frac{\mathrm{load}}{\mathrm{effort}} \\ \Rightarrow 10=\frac{1000}{\mathrm{effort}} \\ \Rightarrow \mathrm{effort}=100\mathrm{kg} \\ \mathrm{according}\mathrm{to}\mathrm{pascal}\text{'}\mathrm{s}\mathrm{law}\mathrm{pressure}\mathrm{on}\mathrm{both}\mathrm{side}\mathrm{will}\mathrm{be}\mathrm{equal} \\ (\mathrm{i}.\mathrm{e})\mathrm{pressure}\mathrm{on}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{effort}\mathrm{applied}=\mathrm{pressure}\mathrm{on}\mathrm{area}\mathrm{of}\mathrm{load}\mathrm{applied} \\ \mathrm{as}\mathrm{pressure}=\frac{\mathrm{force}}{\mathrm{Area}} \\ \Rightarrow \frac{\mathrm{load}}{{\mathrm{Area}}_{\mathrm{L}}}=\frac{\mathrm{effort}}{{\mathrm{Area}}_{\mathrm{e}}}(\text{'}\mathrm{L}\text{'}-\mathrm{load},\text{'}\mathrm{e}\text{'}-\mathrm{effort}) \\ \Rightarrow \frac{1000}{10}=\frac{100}{{\mathrm{Area}}_{\mathrm{e}}} \\ {\mathbf{Area}}_{\mathbf{e}}\mathbf{=}\mathbf{1}{\mathbf{cm}}^{\mathbf{2}} \end{gathered}$$
Hence option (a) is the correct answer.