Q 11-09-115JEE MainJEE Main 2021 (24 Feb, Shift 1)Medium
A hydraulic press can lift 100 kg when a mass $m$ is placed on the smaller piston. It can lift ______ kg when the diameter of the larger piston is increased by 4 times and that of the smaller piston is decreased by 4 times keeping the same mass $m$ on the smaller piston.
Numerical value type. Enter your answer.
Answer: 25600
By Pascal's law $\dfrac{Mg}{A_2} = \dfrac{mg}{A_1}$, so the load lifted is $M = m\dfrac{A_2}{A_1} \propto \dfrac{d_2^2}{d_1^2}$.
New ratio: $\dfrac{(4d_2)^2}{(d_1/4)^2} = 256\dfrac{d_2^2}{d_1^2}$, so $M' = 256\times100 = 25600$ kg.
Solution by Sreeraj P, M.Sc Physics