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Question

An iron rod and another of brass, both at 27C differ in length by 103m. The coefficient of linear expansion for iron is 1.1×105/C and for brass is 1.9×105/C. The temperature at which both these rods will have the same length is


A

0°C

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B

152°C

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C

175°C

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D

Data is insufficient

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Solution

The correct option is A

0°C


The given data is normally insufficient to determine the result. Either the length of one of the rods at 0C must be known or one has to assume that both the rods had the same length at 0C which is not possible if they have the same length again at another temperature. Suppose the two rods had the same length L at 0C. Then by the given problem,

L[1+1.9×105×27]L[1+1.1×105×27] = 103

L×0.8×27×105 = 103

Or L = 1030.8×27×105m = 4.63m

Hence 0C is a possible choice and the rods had equal length of 4.63m at 0C


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