Question

A thin copper wire of length $l\text{metre}$ increases in length by $2\%$ when heated through ${10}^{\circ }C.$ What is the percentage increase in area , when a square copper sheet of length $l\text{metre}$ is heated through ${10}^{\circ }C$ ?

• A. $4\%$
• B. $8\%$
• C. $16\%$
• D. None of the above

Answer 1

The correct option is A $4\%$

Given,
Percentage increment in length is
$\frac{\Delta l}{l}\times 100=+2$
$\Rightarrow \frac{\Delta l}{l}=0.02$
For square copper sheet,
Area $A=l^2$
By taking logarithm and differentiating we get,
$\frac{\Delta A}{A}=2\frac{\Delta l}{l}$
Percentage error can be written as,
$\frac{\Delta A}{A}\times 100=2\times \frac{\Delta l}{l}\times 100$
$\Rightarrow \%$ change in Area $=2\times 2=+4\%$
Thus, option $\left(a\right)$ is the correct answer.