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. `alpha_(1)l_(2) = a_(2)l_(1)`
B. `alpha_(1)l_(2)^(2)= alpha_(2)l_(1)^(2)`
C. `alpha_(1)^(2)l_(2) = alpha_(2)^(2) l_(1)`
D. `alpha_1l_(1)= alpha_2l_2`

Answer

D

Explanation

`Delta l_(1) = Delta l_(2)`
`rArr l_1 alpha_1 Delta T = l_2 alpha_2 Delta T`
`rArr l_1 alpha_1 = l_2 alpha_2`.