In the shown planar frame made of thin uniform rods, the length of section `AB` and `EF` is `l_(1)` and its thermal linear coefficient of expansion is `alpha_(1)`. The length of section `CD` is `l_(2)` and its thermal linear coefficient of expansion is `alpha_(2)`.`CB and DE` are of same length having thermal linear coefficient of expansion `alpha_(2)`. point `A, B, E and F` reside on same line, that is, sections `AB and EF` overlap. then the ratio of `(l_(1))/(l_(2)` for which the distance between end `A` and end `F` remains the same at all temperatures, is

Options

A. `(alpha_(2))/(2alpha_(1))`
B. `(2alpha_(2))/(alpha_(1))`
C. `(2alpha_(1))/(alpha_(2))`
D. `(alpha_(1))/(2alpha_(2))`

Answer

A

Explanation

For distance between `A` and `F` to remain constant, extension in `CD` = extension in `AB` +extension in `EF`
`:. Delta l_(2) = 2 Delta l_(1) rArr l_(2)alpha_(2)Delta theta_(2) = 2l_(1)alpha_(1)Delta theta`
or, `(l_(1))/(l_2) = (alpha_2)/(2alpha_1)`.