A meter scale made of steel is calibrated at `20^@C` to give correct reading. Find the distance between 50 cm mark and 51 cm mark if the scale is used at `10^@C`. Coefficient of linear expansion of steel is `1.1 xx 10^(-5)C^(-1)`

Explanation

`t_1=20^0C`
`t_2=10^0C`
`L _1= 1 cm =0.01m`
`L_2=?`
`alpha _steel = 1.1xx 10^-5/ ^0C`
`L_2=L _1 (1+ alpha_steel Delta T )`
`=0.01(1+1.1xx 10^-5xx10)`
`=0.01+0.01xx1.1xx10^-4`
`=10^-2+10^-2xx1.1xx10^-4`
`=10^-2+1.1xx 10^-6`
`= 10^4 xx 10^-6+ 1.1xx 10^-6`
`=10^-6(10000+1.1)= 10001.1`
`= 1.00011xx 10^-2m`
`=1.00011 cm`