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A force $F$ is applied on a square plate of length $L$. If the percentage error in the determination of $L$ is $3 \%$ and in $F$ is $4 \%$, then permissible error in the calculation of pressure is
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Verified Answer
The correct answer is:
$10 \%$
Given,
Percentage error in length $=3 \%$
Percentage error in force $=4 \%$
We know that,
Pressure, $\quad P=\frac{F}{A}$
Area of square $=(L)^2$
$\begin{aligned}
P & =\frac{F}{L^2} \\
\frac{\Delta P}{P} & =\frac{\Delta F}{F}+\frac{2 \Delta L}{L} \\
\left(\frac{\Delta P}{P} \times 100\right) & =\left(\frac{\Delta F}{F} \times 100\right)+2\left(\frac{\Delta L}{L} \times 100\right) \\
& =4 \%+2(3 \%)=10 \%
\end{aligned}$
Percentage error in length $=3 \%$
Percentage error in force $=4 \%$
We know that,
Pressure, $\quad P=\frac{F}{A}$
Area of square $=(L)^2$
$\begin{aligned}
P & =\frac{F}{L^2} \\
\frac{\Delta P}{P} & =\frac{\Delta F}{F}+\frac{2 \Delta L}{L} \\
\left(\frac{\Delta P}{P} \times 100\right) & =\left(\frac{\Delta F}{F} \times 100\right)+2\left(\frac{\Delta L}{L} \times 100\right) \\
& =4 \%+2(3 \%)=10 \%
\end{aligned}$
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