Answer:
The force on the output piston is 4 times of the force on the input piston.
Explanation:
Given that,
The diameter of the input piston, [tex]d_1=2\ cm[/tex]
The radius of the input piston, [tex]r_1=1\ cm[/tex]
The diameter of the output piston, [tex]d_2=4\ cm[/tex]
The radius of the output piston, [tex]r_2=2\ cm[/tex]
According to Pascal's law, the pressure at smaller piston is equal to the pressure at larger piston such that,
[tex]\dfrac{F_1}{A_1}=\dfrac{F_2}{A_2}\\\\\dfrac{F_2}{F_1}=\dfrac{A_2}{A_1}\\\\\dfrac{F_2}{F_1}=\dfrac{\pi r_2^2}{\pi r_1^2}\\\\\dfrac{F_2}{F_1}=\dfrac{r_2^2}{r_1^2}\\\\\dfrac{F_2}{F_1}=\dfrac{2^2}{1^2}\\\\\dfrac{F_2}{F_1}=\dfrac{4}{1^2}\\\\F_2=4\times F_1[/tex]
So, the force on the output piston is 4 times of the force on the input piston.
