Question

A piston of cross-sectional area $100c{m}^2$ is used in a hydraulic press to exert a force of ${10}^7$ dyne on the water. The cross sectional area of the other piston which supports an object having a mass of $2000kg$ is

• A. $100c{m}^2$
• B. ${10}^{9}c{m}^2$
• C. $2\times {10}^{4}c{m}^2$
• D. $2\times {10}^{10}c{m}^2$

Answer 1

The correct option is C $2\times {10}^{4}c{m}^2$

By Pascal's law, the pressure increased using one piston is communicated everywhere in the fluid. Thus, the same pressure acts on the other piston.

Cross-sectional area of piston 1 is $A_1=100{\text{cm}}^2=0.01{\text{m}}^2$

Force on piston 1 is $F_1={10}^7\text{dyne}=100\text{N}$

Force on piston 2 is $F_2=2000\text{kg wt}=2000\times 10=2\times {10}^4\text{N}$

Let the cross-sectional area of Piston 2 be $A_2=A$.

By Pascal's law, $P_1=P_2\Rightarrow \frac{F_1}{A_1}=\frac{F_2}{A_2}\Rightarrow A_2=\frac{F_2{A}_1}{F_1}\Rightarrow A=\frac{2\times {10}^4\times 0.01}{100}=2{\text{m}}^2=2\times {10}^4{\text{cm}}^2$