Question

A hydraulic lift is shown in the figure. The radii of the movable pistons \(P_1\) and \(P_2\) are \(2\,\text{m}\) and \(8\,\text{m}\) respectively. If a body of mass \(2\,\text{kg}\) is placed on piston \(P_1\), then the force on piston \(P_2\) is \((\text{Ignore atmospheric pressure, acceleration due to gravity}=10\,\text{m s}^{-2})\)

• A. \(320\,\text{N}\)
• B. \(80\,\text{N}\)
• C. \(1280\,\text{N}\)
• D. \(20\,\text{N}\)

Hint:

In a hydraulic lift, \[ \frac{F_1}{A_1}=\frac{F_2}{A_2}. \] Since \(A=\pi r^2\), the force multiplication factor is \[ \frac{F_2}{F_1}=\frac{r_2^2}{r_1^2}. \]

Answer 1

The Correct Option is A

Step 1: State Pascal's principle for hydraulic systems.
Pressure is transmitted equally: F₁/A₁ = F₂/A₂.

Step 2: Compute force on smaller piston.
F₁ = mg = 2 × 10 = 20 N.

Step 3: Find area ratio from radii.
A₂/A₁ = (r₂/r₁)² = (8/2)² = 16.

Step 4: Calculate force on larger piston.
F₂ = F₁ × (A₂/A₁) = 20 × 16 = 320 N.

Step 5: Final Answer:
320 N.