Question 31 of 192

A hydraulic press can lift $100kg$ 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.

Your answerCheck answer

Show answer and solution▾

Answer: 25600

Using Pascals law,

$\dfrac{100\times g}{{A}_{2}}=\dfrac{mg}{{A}_{1}}...\left(1\right)$
Let $m$ mass can lift ${M}_{0}$ in second case then
$\dfrac{{M}_{0}g}{16{A}_{2}}=\dfrac{mg}{{A}_{1}/16}...\left(2\right)$
$\left\{SinceA=\dfrac{\pi {d}^{2}}{4}\right\}$
From equation $\left(1\right)$ and $\left(2\right)$ we get
$\dfrac{{M}_{0}}{16.100}=16$
$\Rightarrow {M}_{0}=25600kg$