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JEE Main 2021 (24 Feb, Shift 1) · Density, Compressibility & Pascal's Law

Density, Compressibility & Pascal's Law question from JEE Main 2021 (24 Feb, Shift 1)

Q16JEE Main 2021 · 24 FEB · SHIFT 1Easy

Density, Compressibility & Pascal's Law

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 answer type. Work it out, then open the answer.

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Answer: 25600

  1. Load lifted M=mA2A1=m(Dd)2M = m\dfrac{A_2}{A_1} = m\left(\dfrac{D}{d}\right)^2.
  2. New ratio: 4Dd/4=16Dd\dfrac{4D}{d/4} = 16\dfrac{D}{d}, so area ratio becomes 162=25616^2 = 256 times larger.
  3. M′=100×256=25600 kgM' = 100\times256 = 25600\text{ kg}
  4. So it can lift 25600 kg.
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