A hydraulic press consists of two cylinders of cross-sectional radius r 1 and r 2 . If a force of 200N applied…

Analyze the question A hydraulic press works on Pascal's principle: pressure applied to a fluid in a closed system is transmitted equally throughout the fluid. We are asked for the ratio of the radii r₁ : r₂, given the input and output forces.

Concept Pressure is the same on both pistons:

F₁/A₁ = F₂/A₂

Since the area of a circular piston is A = πr², this becomes:

F₁/(πr₁²) = F₂/(πr₂²)

so F₂/F₁ = r₂²/r₁²

Solution

• F₁ = 200 N, F₂ = 3200 N
• F₂/F₁ = 3200/200 = 16

So r₂²/r₁² = 16

Taking the square root: r₂/r₁ = 4

Therefore r₁ : r₂ = 1 : 4

Answer The ratio is 1:4, which is option A.

Tip Force ratio is the ratio of areas, not radii. Since area depends on the radius squared, always take the square root of the force ratio to get the radius (or diameter) ratio. Here, 16 becomes 4. Option D (1:16) is the trap for students who forget to take the square root.