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 answer
    A
    $7 \%$
  • 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'.

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