A meter scale is made of steel reads accurately at `20^@C`. In a sensitive experiment, distance accurate up to 0.055 mm in 1 m are required. Find the range of temperature in which the experiment can be performed with this meter scale. Coefficient of linear expansion of steel `=11 xx 10^(-6 @)C^(-1)`.

Explanation

`T_1=20^0C`
`Delta L= 0.055mm `
`=0.055xx 10^-3m`
`T_2=?`
`alpha_st= 11xx 10^-6/^0C`
we know `Delta L= L_0 alpha delta T`
`rArr 0.055xx10^-3=1 xx 11 xx10^-6 xx (T_1 +- T_2)`
`rArr 5xx10^-3 =(20pm T_2) xx 10_3`
`rArr 20 pm T_2 = 5`
`rArr T_2 =20+5=25^0C`
or `20 -5 = 15^0C`
hence the experiment can be performed from `15^0C to 25^0C`.