The coefficient of linear expansion of an in homogeneous rod change linearly from `alpha_(1)` to `alpha_(2)` from one end to the other end of the rod. The effective coefficient of linear expansion of rod is

Options

A. `alpha_1+alpha_2`
B. `(alpha_1+alpha_2)/(2)`
C. `sqrt(alpha_1alpha_2)`
D. `alpha_1-alpha_2`

Answer

B

Explanation

The effective value of `alpha` at a distance x from the left end is
`alpha_x=alpha_1+((alpha_2+alpha_1)/(L))x`
`DeltaL=int_0^Lalpha_xdxDeltat`
`L=((alpha_1+alpha_2)/(2))LDeltaT`
`alpha_("eff")=(alpha_1+alpha_2)/(2)`