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The pressure on a circular plate is measured by measuring the force on the plate and the radius of the plate. If the errors in measurement of the force and the radius are $5 \%$ and $3 \%$ respectively, the percentage of error in the measurement of pressure is
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The correct answer is:
$11$
We have
$\begin{aligned}
& p=\frac{F}{A}=\frac{F}{\pi R^2} \\
& \text { So, } \frac{\Delta p}{p} \times 100=\frac{\Delta F}{F} \times 100+2 \frac{\Delta R}{R} \times 100 \\
& =5+2(3)=5+6=11 \\
& \Rightarrow \frac{\Delta p}{p} \times 100=11 \%
\end{aligned}$
$\begin{aligned}
& p=\frac{F}{A}=\frac{F}{\pi R^2} \\
& \text { So, } \frac{\Delta p}{p} \times 100=\frac{\Delta F}{F} \times 100+2 \frac{\Delta R}{R} \times 100 \\
& =5+2(3)=5+6=11 \\
& \Rightarrow \frac{\Delta p}{p} \times 100=11 \%
\end{aligned}$
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