What is the force needed to apply to a piston of 2 cm radius in order to result a force of 6000 N at the working piston of radius 6 cm ?

Concept:

Pascal’s Law: It is also known as principle of transmission of fluid pressure.

As per the law:

Pressure applied at piston = Pressure exerted on the working piston

\(\frac{{{F_1}}}{{{A_1}}} = \frac{{{F_2}}}{{{A_2}}}\)

Calculation:

Given:

Piston radius r1 = 2 cm,

Working piston force F2 = 6000 N, Working piston radius r2 = 6 cm

\(\frac{{{F_1}}}{{{A_1}}} = \frac{{{F_2}}}{{{A_2}}}\)

\(\frac{{{4F_1}}}{{{\pi d_1^2}}} = \frac{{{4F_2}}}{{{\pi d_2^2}}}\)

\(\frac{{{F_1}}}{{{r_1^2}}} = \frac{{{F_2}}}{{{r_2^2}}}\)

\(\frac{{{F_1}}}{{{2^2}}} = \frac{{{6000}}}{{{6^2}}}\)

\({{{F_1}}}{{{}}} = \frac{{{6000}}}{{{36}}}\times4=666.67\;N\)