Q102 / 150 · MHT CET 2025 (25 Apr Shift 2) · Physics
A force $F$ is applied on a square plate of side $L$. If the percentage error in determining F is $3 \%$ and that in L is $2 \%$, then the percentage error in determining the pressure is
- Correct answerA$7 \%$
- B$5 \%$
- C$3 \%$
- D$2 \%$
Solution
The pressure is defined as $P = F / A$, where for a square plate $A = L^2$, giving $P = F / L^2$.
Using the propagation of errors formula $\frac{\Delta P}{P} \times 100\% = \left(1 \cdot \frac{\Delta F}{F} + 2 \cdot \frac{\Delta L}{L}\right) \times 100\%$, and substituting the given errors $\frac{\Delta F}{F} \times 100\% = 3\%$ and $\frac{\Delta L}{L} \times 100\% = 2\%$, we obtain:
$\frac{\Delta P}{P} \times 100\% = (1 \cdot 3\% + 2 \cdot 2\%) = 3\% + 4\% = 7\%$.
Final answer: $\boxed{\text{A}}$
Hence, the correct answer is option: 'A'.