A piece of metal weight 45 g is air and 25 g in a liquid of density `1.5 xx 10^(3)kg-m^(-3)` Kept at `30^(@)`. When the temperature of the liquid is raised to `40^(@)C`, the metal piece weight 27g. The density of liquid at `40^(@)C` is `1.25 xx 10^(3) kg-m^(-3)`. The coefficient of linear expansion of metal is

Options

A. `1.3xx10^(-3)//""^(@)C`
B. `5.2xx10^(-3)//""^(@)C`
C. `2.6xx10^(-3)//""^(@)C`
D. `0.26xx10^(-3)//""^(@)C`

Answer

C

Explanation

`V_(1)=((45-25)g)/(d_(1)) and V_(2)=((45-27)g)/(d_(2))`
`therefore (V_(1))/(V_(2))=(20)/(18)xx(d_(2))/(d_(1))`
or `(V_(1))/(V_(1)(1+r_("metal")xx10))=(20)/(18)xx[(d_(1))/((1+r_(l)xx10)d_(1))]`
After simplifying, we get `alpha=(gamma_("metal"))/(3)=2.6xx10^(-3)//""^(@)C`