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Question
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%, the permissible error in the calculation of pressure is ______.
Options
13%
10%
7%
12%
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Solution
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%, the permissible error in the calculation of pressure is 10%.
Explanation:
\[\begin{aligned} \text{Pressure (P)} & =\frac{\mathrm{Force}\left(\mathrm{F}\right)}{\mathrm{Area}\left(\mathrm{A}\right)} \\ & =\frac{\mathrm{F}}{\mathrm{L}^{2}} \end{aligned}\] \[\begin{aligned} & & ....(\because\mathrm{Area}=\mathrm{length}^{2}) \\ \mathrm{Percentage~error~in~pressure~is~given~by,} \\ :\quad{\frac{\Delta P}{P}}\times100={\frac{\Delta F}{F}}\times100+2{\frac{\Delta L}{L}}\times100 \\ & & =4\%+2(3\%)=4\%+6\%=10\% \end{aligned}\]
