An iron rod of length 50 cm is joined at an end to aluminium rod of length 100 cm. All measurements refer to `20^(0) C` . Find the length of the composite system at `100^(o) C` and its average coefficient of linear expansion. The coefficient of linear expansion of iron and aluminium are `12 X 10^(-6 ) C^(-1)` and `24 X10^(-6 ) C ^(-1)` respectively.

Options

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

Answer

C

Explanation

Initially (at `20^@C`) length of composite system `L=50+100=150cm`
Length of iron rod at `100^@C=50[1+12xx10^-6xx(100-20)]=50.048cm`
Length of aluminium rod at `100^@C=100[1+24xx10^-6xx(100-20)]=100.192cm`
Finally (at `100^@C`) length of the composite system `L'=L'-L=150.24-150=0.24cm`
Average coefficient of expansion at `100^@C`
`alpha=(DeltaL)/(LxxDeltaT)=(0.24)/(150xx(100-20))=20xx10^(-6)//^(@)C`