Question

The movable cylindrical pistons \(P_1\) and \(P_2\) of a hydraulic lift are of radii \(2\ \text{m}\) and \(R\) respectively. A body of mass \(32\ \text{kg}\) on piston \(P_2\) is supported by a body of mass \(2\ \text{kg}\) placed on piston \(P_1\). The value of \(R\) is

• A. \(8\ \text{m}\)
• B. \(32\ \text{m}\)
• C. \(2\ \text{m}\)
• D. \(16\ \text{m}\)

Hint:

In a hydraulic lift, pressures on both pistons are equal: \[ \frac{F_1}{A_1}=\frac{F_2}{A_2}. \] Since piston area is proportional to the square of radius, use \[ A=\pi r^2. \]

Answer 1

The Correct Option is A

Step 1: Apply Pascal's law.
Pressure is equal on both pistons: \( \frac{F_1}{A_1} = \frac{F_2}{A_2} \). \( F_1 = 2g \), \( F_2 = 32g \), \( r_1 = 2\,\text{m} \).

Step 2: Solve for R.
\[ \frac{2}{\pi(4)} = \frac{32}{\pi R^2} \Rightarrow R^2 = \frac{32\times4}{2} = 64 \Rightarrow R = 8\,\text{m} \] \[ \boxed{8\,\text{m}} \]