An iron rod and another of brass, both at `27^@C` differ in length by `10^-3`m. The coefficient of linear expansion for iron is `1.1xx10^(-5)//^(@)C` and for brass is `1.9xx10^(-5)//^(@)C`. The temperature at which both these rods will have the same length is

Options

A. `0^@C`
B. `152^@C`
C. `175^@C`
D. Data is insufficient

Answer

A

Explanation

The given data is normally isufficient to determine the result. Either the length of one of the rods at `0^@C` must be known or one has to assume that both the rods had the same length at `0^@C` which is not possible if they have the same length again at another temperature. Suppose the two rods had the same length L at `0^@C`. Then by the given problem
`L[1+1.9xx10^-5xx27]-L(1+1.1xx10^-5xx27]=10^-3`
`Lxx0.8xx27xx10^-5=10^-3`
or `L=(10^-3)/(0.8xx27xx10^-5)m=4.63m`
Hence `0^@C` is a possible choice and the rods had equal length of `4.63m` at `0^@C`.