A thin copper wire of length lmetre increases in length by 2% when heated through 10∘C. What is the percentage increase in area , when a square copper sheet of length lmetre 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 A4% 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.