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Question
A metre scale made of steel is calibrated at 20∘C to give correct reading. Find the distance between 50 cm mark and 51 cm mark if the scale is used at 10∘C. Coefficient of linear expansion of steel is 1.1×10−5 ∘C−1
A metre scale made of steel is calibrated at 20∘C to give correct reading. Find the distance between 50 cm mark and 51 cm mark if the scale is used at 10∘C. Coefficient of linear expansion of steel is 1.1×10−5 ∘C−1
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Solution
t1=20∘C
t2=10∘C
L1 = 1 cm = 0.01 m
L2 = ?
αsteel=1.1×10−5/ ∘C
L2=L1 (1+αsteel ΔT)
=0.01(1+1.1×10−5×10)
=0.01+0.01×1.1×10−4
=10−2+10−2×1.1×10−4
=10−2+1.1×10−6
=104×10−6+1.1×10−6
=10−6 (10000 + 1.1) = 10001.1
= 1.00011 ×10−2m
= 1.00011 cm
t1=20∘C
t2=10∘C
L1 = 1 cm = 0.01 m
L2 = ?
αsteel=1.1×10−5/ ∘C
L2=L1 (1+αsteel ΔT)
=0.01(1+1.1×10−5×10)
=0.01+0.01×1.1×10−4
=10−2+10−2×1.1×10−4
=10−2+1.1×10−6
=104×10−6+1.1×10−6
=10−6 (10000 + 1.1) = 10001.1
= 1.00011 ×10−2m
= 1.00011 cm
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