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. `1.3 xx 10^(-3)//^(@)C`
B. `5.2 xx 10^(-3)//^(@)C`
C. `2.6 xx 10^(-3)//^(@)C`
D. `0.26 xx 10^(-3)//^(@)C`

Answer

C

Explanation

`Volume = (Mass(m))/(Density (p))=(w)/(pg)`
Volume of metal piece at `30^(@)C(V_(30)^(@))=((45-25))/(1.5xxg)cm^(3)`
Volume of metal piece at `40^(@)C(V40^(@))=((45-27))/(1.25g)cm^(3)`
Coefficient of cubical expansion (`gamma)`= `(V_(40^(@))-V_(30^(@)))/(V_(40^(@)(Deltat)`
`=14.4-13.33`
`14.4(10)`
`=8xx10^(-3@)C`
Coefficient of cubical expansion`(alpha)` `= (gamma)/(3)=0.003`
`cong2.6xx10^(-3)//^(@)C`