Question

An iron rod of length 100m at 10°C used to measure a distance of 2km on a day when the temperature is 40°C. Calculate the error in measuring the distance?

Answer 1

We know that when an object is heated or cooled, its length changes by an amount `dl` which is proportional to the original length `L_0` and the change in temperature `Deltat`. This can be expressed as

`dl = L_0\ α\ (t_f - t_i)` .............(1)
where `α` is coefficient of linear expansion, `t_i` initial temperature and `t_f`.

Taking `alpha` for forged iron rod as `1.13xx10^-5\ K^-1` change in length of rod is

`dl = 100xx 1.13xx10^-5\ (40 - 10)`
`dl=0.0339\ m`

Distance measured `=2000\ m`
Error in measurement `epsilon=2000/(100+0.0339)xx0.0339`
`=>epsilon=0.68\ m`