A liquid filled sealed system has cylinders with movable pistons on each end. The face of one piston has an area of 5 cm². The other piston has an area of 500 cm² and is supporting a weight of 2 kN on it. What force must be applied to the small cylinder to hold the weight up?
a. 200N
b. none of these
c. 2000 N
d. 20N

Option D is correct.

The force that must be applied to the small cylinder to hold the weight up is 20N

Explanation:

For the force to hold the smaller cylinder up, the pressure exerted on/by the pistols must be equal.

Let the pressure on the big cylinder be P₁, the force exerted F₁ = 2kN = 2000N and the area A₁ = 500 cm²

Let the pressure on the small cylinder be P₂, the force exerted F₂ = ? and the area A₂ = 5 cm²

Since the two Areas are in the same units, no need to convert to SI units.

P₁ = P₂

F₁/A₁ = F₂/A₂

2000/500 = F₂/5

F₂ = 2000 × 5/500 = 20N

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