Question

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

• A. 32 m
• B. 2 m
• C. 16 m
• D. 8 m

Hint:

Use Pascal's Law to relate pressure in hydraulic systems. Set \(\frac{F}{A}\) equal on both pistons to find unknown quantities.

Answer 1

The Correct Option is D

We apply Pascal's law, which states that pressure is the same on both pistons of the hydraulic lift: \[ \text{Pressure at } P_1 = \frac{F_1}{A_1} = \frac{m_1 g}{\pi r_1^2}, \quad \text{Pressure at } P_2 = \frac{F_2}{A_2} = \frac{m_2 g}{\pi R^2} \] Given: \[ m_1 = 2\,\text{kg}, \quad r_1 = 2\,\text{m}, \quad m_2 = 32\,\text{kg} \] Equating pressures: \[ \frac{2g}{\pi \cdot 4} = \frac{32g}{\pi R^2} \Rightarrow \frac{1}{2} = \frac{32}{R^2} \Rightarrow R^2 = 64 \Rightarrow R = 8\,\text{m} \]