Question

Piston of cross-section area ${100cm}^2$ is used in a hydraulic press to exert a force ${10}^7$ dynes on the water. The cross-sectional area of the piston which support an object having a mass 2000 kg is

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

Answer 1

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

According to Pascal Law

$P_1=P_2\frac{F_1}{A_1}=\frac{F_2}{A_2}$

GIVEN,

$F_1={10}^{7}dyne=100N$

$A_1=100c{m}^2$

$F_2=Mg=2000\times 10=2\times {10}^{4}N$

Now,

$P_1=P_2\frac{F_1}{A_1}=\frac{F_2}{A_2}$

Substitute all value in above equation

$\frac{100}{100}=\frac{2\times {10}^4}{A_2}100A_2=200\times {10}^4{A}_2=\frac{200\times {10}^4}{100}=2\times {10}^4{cm}^2$

Option (C) is correct option