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.
JEE MAIN 2021, Diffcult
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Using Pascals law
$\frac{100 \times g }{ A _{2}}=\frac{ mg }{ A _{1}}$ $........(1)$
Let $m$ mass can lift $M _{0}$ in second case then
$\frac{ M _{0} g }{16 A _{2}}=\frac{ mg }{ A _{1} / 16}$ $.........(2)$
$\left\{\right.$ Since $\left.A=\frac{\pi d ^{2}}{4}\right\}$
From equation $(1)$ and $(2)$ we get
$\frac{ M _{0}}{16.100}=16$
$\Rightarrow M _{0}=25600 \,kg$
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