The length of two metallic rods at temperatures `theta` are `L_(A)` and `L_(B)` and their linear coefficient of expansion are `alpha_(A)` and `alpha_(B)` respectively. If the difference in their lengths is to remain constant at any temperature then

Options

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

Answer

B

Explanation

Change in `L_(A)` = change in `L_(B)`
i.e., `Delta L_(A) = L_(B)`
`rArr alpha_(A)Delta T L_(A)=alpha_(B)Delta T L_(B)`
or, `alpha_(A)L_(A)=alpha_(B)L_(B)`.