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A hydraulic press containing water has two vertical arms joined at the bottom. As shown in the figure, the thicker arm has diameter 14 cm and the thinner arm has diameter 1.4 cm. A force of 10 N is applied downward on the surface of the water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is ______ N.

Asked in JEE Main 5th April 2nd Shift 2024 · Pascal's law and hydraulics

Figure: Pascal's law and hydraulics
Answer: 1000

Step-by-step solution

Given: d₁=1.4 cm (thin arm, carrying f=10 N) and d₂=14 cm (thick arm).

For equilibrium the pressure applied at the two surfaces must match, f/a=F/A, so F=fA/a.

Area goes as the square of the diameter: A/a=((d₂)/(d₁))²=((14)/(1.4))²=100.

F=10×100=1000 N.

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