Q. In a hydraulic press the small cylinder has a diameter of $'d_{1}^{'}\ cm$, while the large piston has a diameter of $'d_{2}'cm$. If a force $'F_{1}'$ is applied to a small piston, the force on the large piston $'F_{2}'$ is given by
A) $F_{2} = \frac{d_{2}^{2}}{d_{1}^{2}}F_{1}$
B) $F_{2} = \frac{d_{1}^{2}}{d_{2}^{2}}F_{1}$
C) $F_{2} = \frac{d_{1}^{2}}{d_{2}^{2}}\frac{1}{F_{1}}$
D) $F_{2} = \frac{d_{2}^{2}}{d_{1}^{2}}\frac{1}{F_{1}}$
Explanation
(a) Using Pascal’s law
$P_{1} = P_{2} \Rightarrow \frac{F_{1}}{\left( \frac{\pi d_{1}^{2}}{4} \right)} = \frac{F_{2}}{\left( \frac{\pi d_{2}^{2}}{4} \right)} \Rightarrow F_{2} = \frac{d_{2}^{2}}{d_{1}^{2}}F_{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.