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Question

What is the percentage change in length of 1m iron rod if the temperature change by 100C (Assume coefficient of linear expansion, α=2×105C1)


A

0.1%

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B

0.2%

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C

0.3%

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D

0.4%

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Solution

The correct option is B

0.2%


Given:
Length of rod, l=1m and change in temperature, ΔT=100C
Coefficient of linear expansion of iron rod, α=2×105C1
Now,
l1=l(1+αΔT)
where, l1 is the final length of the iron rod, l is the original length of the iron rod, α is the coefficient of linear expansion of iron rod and ΔT is the change in temperature of iron rod.
or, l1l=l×α×ΔT
or, Δll=αΔT=2×105×100
or, Δll=2×103
Therefore, % change in length =Δll×100=2×103×100=0.2%

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