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Question

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

A
4%
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B
8%
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C
16%
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D
None of the above
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Solution

The correct option is A 4%
Given,
Percentage increment in length is
Δll×100=+2
Δll=0.02
For square copper sheet,
Area A=l2
By taking logarithm and differentiating we get,
ΔAA=2Δll
Percentage error can be written as,
ΔAA×100=2×Δll×100
% change in Area =2×2=+4 %
Thus, option (a) is the correct answer.

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