An iron rod of length 50 cm is joined at an end to an aluminum rod of length 100 cm. All measurements refer to `20^(@)C` . The coefficients of linear expansion of iron and aluminum are `12xx10^(-6)//^(@)C and 24xx10^(-6)//^(@)C`, respectively. The average coefficient of expansion of composite system is :

Options

A. `36xx10^(-6)//^(@)C`
B. `12xx10^(-6)//^(@)C`
C. `20xx10^(-6)//^(@)C`
D. `48xx10^(-6)//^(@)C`

Answer

C

Explanation

`l_(1)+l_(2)=l_(0)(l+alpha_(1)DeltaT)+l_(0)(1+alpha_(2)DeltaT)`
`l_(1)+l_(2)=50(1+alpha_(1)DeltaT)+100(1+alpha_(2)DeltaT)`
`l_(1)l_(2)=150(1+(50alpha_(1)+100alpha_(2))/(150)DeltaT)`
`alpha_(eq)=(50xx12xx10^(-6)+100xx24xx10^(-6))/(150)=12xx10^(-6)((250)/(150))=20xx10^(-6)//^(@)C`