Two rods of length `l_(1)` and `l_(2)` are made of material whose coefficient of linear expansion are `alpha_(1)` and `alpha_(2)` , respectively. The difference between their lengths will be independent of temperatiure if `l_(1)//l_(2)` is to

Options

A. `(l_1)/(l_2)=(alpha_1)/(alpha_2)`
B. `(l_1)/(l_2)=(alpha_2)/(alpha_1)`
C. `l_(1)^(2) alpha_1 = l_(2)^(2) alpha_2`
D. `alpha_1 ^(2) l_1 = alpha _(2)^(2) l_2`

Answer

B

Explanation

For the two rods, the increase in lengths should be same.
` therefore l_1 alpha_1 t =l_2 alpha_2 t or (l_1)/(l_2) = (alpha_2)/(alpha_1)`