Question

A hydraulic lift is shown in the figure. The movable pistons A, B and C are of radius 10 cm, 100 cm and 5 m respectively. If a body of mass 2 kg is placed on piston A, the maximum masses that can be lifted by pistons B and C are respectively:

• A. 200 kg and 500 kg
• B. 20 kg and 50 kg
• C. 200 kg and 5000 kg
• D. 2000 kg and 5000 kg

Hint:

Use Pascal’s principle: \( \frac{F}{A} \) remains constant across pistons in a hydraulic system. Area varies as \( \pi r^2 \).

Answer 1

The Correct Option is C

Using Pascal’s Law: Pressure is transmitted equally, i.e., \[ \frac{F_A}{A_A} = \frac{F_B}{A_B} = \frac{F_C}{A_C} \] Given: - Radius of A = 10 cm, B = 100 cm, C = 500 cm (5 m)
- Mass on A = 2 kg
So force on A: \[ F_A = 2g = 2 \times 10 = 20\, \text{N} \] Area is proportional to \( r^2 \), so: \[ \frac{F_B}{F_A} = \left( \frac{R_B}{R_A} \right)^2 = \left( \frac{100}{10} \right)^2 = 100 \Rightarrow F_B = 100 \cdot 20 = 2000\, \text{N} \Rightarrow m_B = \frac{2000}{10} = 200\, \text{kg} \] \[ \frac{F_C}{F_A} = \left( \frac{500}{10} \right)^2 = 2500 \Rightarrow F_C = 2500 \cdot 20 = 50000\, \text{N} \Rightarrow m_C = \frac{50000}{10} = 5000\, \text{kg} \]