Question

A student uses a metre scale, measuring upto $1mm$, to measure the length an breadth of a retangular plate. He finds that length$=5.7cm$ and breadth $=3.4cm$. What is the percentage error in the area of the plate?

• A. $3.58\%$
• B. $4.7\%$
• C. $5.3\%$
• D. $6.2\%$

Answer 1

The correct option is B $4.7\%$

$\begin{array}{c}Given\to \text{Measuring scale with least count}1mm\\ \text{length}=5.7cm=57mm\\ \text{Breadth}=3.4cm=34mm\end{array}$

$\begin{array}{cc}\text{Now}\to \text{Area}& =\text{Length}\times \text{Bredth.}\\ A& =l\times b=57\times 34=1938{mm}^2\end{array}$

$\begin{array}{c}\text{Using error analysis}\to \\ \text{Take logarithm both sides}\\ \log A=\log \left(l\right)+\log \left(b\right)\end{array}$

$\begin{array}{c}\text{difterentiate both sides -}\\ \frac{dA}{A}=\frac{dl}{l}+\frac{db}{b}\Rightarrow dA=A[\frac{dl}{l}+\frac{db}{b}]\end{array}$

$\frac{dA}{A}=1938[\frac{1}{57}+\frac{1}{34}]=0.047=4.7\%$