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

Length of iron rod at `100^@C`
`L_1=50[1+12xx10^-6xx(100-20)]=50.048cm`
Length of aluminum rod at `100^@C`,
`L_2=100[1+24xx10^-6xx(100-20)]=100.192cm`
The length of composite system at `23^@C`
`=50+100=150cm`
and length of composite system at `100^@C`
`=50.048+100.192=150.24cm`
Average`alpha=(0.24cm)/(150cmxx(100-20))`
`=20xx10^(-6)//^@C`
The above shortcut is applicable only if `alpha` varies linearly.