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QJEEM21Ph7a3a: JEE Main 2021 Physics - Class 11 JEEM21Ph7a3a Solution: A hydraulic press can lift 100 kg when a mass 'm' is placed on…

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.

Step-by-Step Verified Solution

According to Pascal's law,

F1A1=F2A2{{{F_1}} \over {{A_1}}} = {{{F_2}} \over {{A_2}}}

Initially, 100gA1=mgA2{{100g} \over {{A_1}}} = {{mg} \over {{A_2}}} .... (i)

Finally, Mg16A1=mg(A216){{Mg} \over {16{A_1}}} = {{mg} \over {\left( {{{{A_2}} \over {16}}} \right)}} ..... (ii)

On dividing Eqs. (i) by (ii), we get

100×16M=116{{100 \times 16} \over M} = {1 \over {16}}

∴\therefore M = 25600 kg

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