Question

In a hydraulic lift, if the radius of the smaller piston is \(5 \ \text{cm}\), and the radius of the larger piston is \(50 \ \text{cm}\), then the weight that the larger piston can support when a force of \(250 \ \text{N}\) is applied to the smaller piston is

• A. \(50 \ \text{kN}\)
• B. \(100 \ \text{kN}\)
• C. \(40 \ \text{kN}\)
• D. \(25 \ \text{kN}\)

Hint:

In hydraulic systems, force multiplies with area. Since area \(A \propto r^2\), a tenfold increase in radius results in a hundredfold increase in force.

Answer 1

The Correct Option is D

Step 1: Use Pascal’s Principle
According to Pascal's law: \[ \frac{F_1}{A_1} = \frac{F_2}{A_2} \Rightarrow F_2 = F_1 \cdot \frac{A_2}{A_1} \] Step 2: Area is proportional to the square of the radius
\[ \frac{A_2}{A_1} = \left( \frac{R_2}{R_1} \right)^2 = \left( \frac{50}{5} \right)^2 = 100 \] Step 3: Calculate force on the larger piston
\[ F_2 = 250 \ \text{N} \times 100 = 25000 \ \text{N} = 25 \ \text{kN} \]