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Question

A rod is measured at 10C using a scale calibrated at that temperature. Find the percentage error in length, if thermal coefficients of linear expansion of the rod and scale are 3×105/C and 2×105/C respectively, and the rod is measured at 50C.

A
0.01 %
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B
0.02 %
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C
0.03 %
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D
0.04 %
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Solution

The correct option is D 0.04 %
Let the length of the rod at temperature T0 [actual length] be L0
α0=3×105/C
αs=2×105/C
T0=10C
T=50C
Measured length at temperature T
L=L0[1+(α0αs)(TT0)]
Percentage error =(LL0L0)×100
=[L0[1+(α0αs)(TT0)]L0L0]×100
=[(α0αs)(TT0)]×100
=[(105)(40)]100
=4×102
=0.04 %

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