JEE PYQ: Mechanical Properties Of Fluids Question 7
Question 7 - 2021 (24 Feb 2021 Shift 1)
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.
Show Answer
Answer: 25600
Solution
Atmospheric pressure $P_0$ will be acting on both the limbs of hydraulic lift. Applying Pascal’s law for same liquid level: $P_0 + \frac{mg}{A_1} = P_0 + \frac{(100)g}{A_2}$
$\Rightarrow \frac{Mg}{A_1} = \frac{(100)g}{A_2} \Rightarrow \frac{m}{100} = \frac{A_1}{A_2}$ …(1)
Diameter of piston on side of 100 kg is increased by 4 times so new area = $16A_2$ Diameter of piston on side of (m) kg is decreasing: $A_1’ = \frac{A_1}{16}$ Again, $\frac{mg}{A_1/16} = \frac{M’g}{16A_2} \Rightarrow \frac{256m}{M’} = \frac{A_1}{A_2}$ From equation (1): $\frac{256m}{M’} = \frac{m}{100} \Rightarrow M’ = 25600$ kg
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