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Question

A brass rod at 30C is observed to be 100 cm long when measured by a steel scale which is correct at 0C. α for steel is 12×106/C and α for brass is 19×106/C. The correct length of brass rod at 0C is :

A
100.021 cm
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B
99.979 cm
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C
100.042 cm
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D
99.958 cm
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Solution

The correct option is D 99.979 cm
As steel scale is correct at 0℃.
Actual length measured by steel scale at 30℃.
L=100(1+t×α)L=100(1+12×106×30)L=100(1.00036)cmL=100.036cm
Brass rod has length 100.036cm at 30℃ let's assume length L' is length at 0℃
so -
100.036=L(1+t×α)100.036=L(1+19×106×30)100.036=L(1.00057)L=99.979cm

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