Coefficient of linear expansion of brass and steel rods are `alpha_(1)` and `alpha_(2)`. Length of brass and steel rods are `l_(1)` and `l_(2)` respectively. If `(l_(2) - l_(1))` is maintained same at all temperature, which one of the following relations holds good?

Options

A. `apha_1 l_2^2`
B. `alpha_1^2 l_2 = alpha_2^2 l_1 `
C. `alpha_1 l_1 = alpha_2 l_2`
D. `alpha_1 l_2 = alpha_2 l_1`

Answer

C

Explanation

Let `l._1` and `l._2` be increase in length of both rods .
Also given `l._2 - l._1 = l_2 - l_1`
`l_2 ( 1 + alpha_2 Delta T) - l_1 (1+ alpha_1 Delta T ) = l_2 - l_1`
` rArr l_1 alpha_1 Delta T = l_1 alpha_2 Delta T`
` alpha_1 l_1 = alpha_2 l_2`