Question

A piston of cross-sectional area \(2.5\times 10^{-2} \text{m}^2\) is used in a hydraulic lift to exert a force of \(250 \text{N}\) on water. The cross-sectional area of the other piston which supports a car of mass \(3000 \text{kg}\) is (\(g = 9.8 \text{m/s}^2\))

• A. \(1.96 \text{m}^2\)
• B. \(2.94 \text{m}^2\)
• C. \(3.92 \text{m}^2\)
• D. \(5.88 \text{m}^2\)

Hint:

Pressure is the same in the fluid, so F1/A1 = F2/A2.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
By Pascal law, pressure applied to an enclosed liquid is transmitted equally, so \(\frac{F_1}{A_1} = \frac{F_2}{A_2}\).

Step 2: Key Formula or Approach:
The load on the second piston is the weight of the car: \(F_2 = mg = 3000 \times 9.8 = 29400\) N.

Step 3: Detailed Explanation:
Pressure in the liquid: \(P = \frac{250}{2.5 \times 10^{-2}} = 10^4\) Pa.
\[ A_2 = \frac{F_2}{P} = \frac{29400}{10^4} = 2.94\ \text{m}^2 \]
The other options correspond to different car masses (\(2000\), \(4000\) and \(6000\) kg).

Final Answer:
The area of the larger piston is \(2.94\) m\(^2\), option (B). \[ \boxed{2.94\ \text{m}^2} \]