The coefficient of linear expansion of brass and steel are `alpha`, and `alpha_(2)` . If we take a brass rod of length `L_(1)`, ar steel rod of length `L_(2)` at `0^(@)`C, their difference in length `(L_(2)-L_(1))` will remain the same at any temperature if

Options

A. `alpha_(1)L_(2) = alpha_(2) L_(1)`
B. `alpha_(1) L_(2)^(2) = alpha_(2)L_(1)^(2) `
C. `alpha_(1)^(2) = alpha_(2)^(2) L_(2)`
D. `alpha_(1) L_(1) = alpha_(2) L_(2)`

Answer

D

Explanation

Difference in lengths of rods will remain same if expansion is same in both the rods. If expansions in first rod is `l_(1) = L_(1) alpha_(1) Delta theta ` and expansion is second rod is `l_(2) = L_(2) alpha_(2) Delta theta` then `L_(1) alpha_(1) Delta theta = L_(2) alpha_(2) Delta theta :. L_(1) alpha_(1) = L_(2) alpha_(2)`