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Question: Answered & Verified by Expert

A hydraulic automobile lift has input and output pistons with diameters of 10 cm and 30 cm. The lift is used to hold up a car with a weight of 1.44×104 N.
What is the force on the input piston?

PhysicsMechanical Properties of FluidsNEET
Options:
  • A 1.6×103 N
  • B 1.5×103 N
  • C 1.4×103 N
  • D 1.8×103 N
Solution:
2528 Upvotes Verified Answer
The correct answer is: 1.6×103 N
Here, the diameter of the input piston, d = 10 cm = 0.1 m

The diameter of output piston, D = 30 cm = 0.3 m

The weight lifted by the output piston, F=1.44×104 N

Let a and A be the areas of a cross-section of the input and output pistons respectively. If f is the force applied on the input piston, then

FA=fa or FπD24=fπd24

Or f=F×d2D2=1.44×104×0.120.32=1.6×103 N

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