Question

A force F is applied on a square plate of side L. If the percentage error in F is 3% and in L is 2%, then the percentage error in pressure is \dots

• A. 7%
• B. 5%
• C. 3%
• D. 2%

Hint:

Remember the golden rule of error analysis: Errors never cancel out; they ALWAYS accumulate! Whether a variable is multiplied ($AB$) or divided ($A/B$), you must always add their percentage errors together.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Pressure is defined as Force per unit Area. For a square plate, Area $A = L^2$.

Step 2: Formula Application:
$P = F/L^2$. In error analysis, for a product or quotient $Z = A^a B^b$, the relative error is $\frac{\Delta Z}{Z} = a\frac{\Delta A}{A} + b\frac{\Delta B}{B}$.

Step 3: Explanation:
$% \text{ Error in } P = (% \text{ Error in } F) + 2 \times (% \text{ Error in } L)$ $% \text{ Error in } P = 3% + 2 \times (2%) = 3% + 4% = 7%$.

Step 4: Final Answer:
The percentage error in pressure is 7%.