Question

The radius of a pump piston and mechanical advantage of a hydraulic press are $0.5\mathrm{m}\mathrm{and}4$m. What is the area of cross section of press piston?

• A. 2
• B. $\pi$
• C. $\frac{\mathrm{\pi }}{4}$
• D. $\frac{\mathrm{\pi }}{2}$

Answer 1

The correct option is B

$\pi$

$$\begin{gathered} \mathrm{mechanical}\mathrm{advantage}\mathrm{of}\mathrm{hydraulic}\mathrm{press}=\frac{\mathrm{area}\mathrm{of}\mathrm{press}\mathrm{piston}}{\mathrm{area}\mathrm{of}\mathrm{pump}\mathrm{piston}} \\ \mathrm{Given}\mathrm{radiys}\mathrm{of}\mathrm{the}\mathrm{pump}\mathrm{piston}=0.5\mathrm{m}=\mathrm{R} \\ \mathrm{mechanical}\mathrm{advantage}\mathrm{of}\mathrm{hydraulic}\mathrm{press}=4 \\ \mathrm{Substitute}\mathrm{these}\mathrm{in}\mathrm{the}\mathrm{formula} \\ 4=\frac{{\mathrm{\pi r}}^2}{{\mathrm{\pi R}}^2}(\mathrm{where}\mathrm{R}\hspace{0.17em}\mathrm{is}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{pump}\mathrm{piston}) \\ \Rightarrow {\mathrm{r}}^2=4\times 0.25=1 \\ \mathrm{Hence}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{cross}\mathrm{section}\mathrm{of}\mathrm{the}\mathrm{press}\mathrm{piston}={\mathrm{\pi r}}^2=\mathrm{\pi }{\mathrm{m}}^2 \end{gathered}$$
Hence option (b) is the correct answer.