Question

A force F is applied onto a square plate of side L. If the percentage error in determining L is 2% and that in F is 4%, the permissible percentage error in determining the pressure is

• A. 2%
• B. 4%
• C. 6%
• D. 8%
• E. 1%

Hint:

When a quantity depends on powers, multiply the percentage error by the power before adding.

Answer 1

The Correct Option is D

Concept: Pressure is defined as: \[ P = \frac{F}{A} \] For a square plate: \[ A = L^2 \Rightarrow P = \frac{F}{L^2} \] Error propagation rule: \[ \frac{\Delta P}{P} = \frac{\Delta F}{F} + 2\frac{\Delta L}{L} \]

Step 1: Write given errors. \[ \frac{\Delta F}{F} = 4%, \quad \frac{\Delta L}{L} = 2% \]

Step 2: Apply error formula. \[ \frac{\Delta P}{P} = 4% + 2 \times 2% = 4% + 4% = 8% \]

Step 3: Final result. \[ \boxed{8%} \]