An equilateral triangle `ABC` is formed by joining three rods of equal length and `D` is the mid-point of `AB`. The coefficient of linear expansion for `AB` is `alpha_(1)` and for `AC` and `BC` is `alpha_(2)`. The relation between `alpha_(1)` and `alpha_(2)`, if distance `DC` remains constant for small changes in temperture is

Options

A. `alpha_(1) = alpha_(2)`
B. `alpha_(1) = 4alpha_(2)`
C. `alpha_(2) = 4alpha_(1)`
D. `alpha_(1) = (1)/(2)alpha_(2)`

Answer

B

Explanation

Before and after changing the tempreature,
`sqrt(l_(2)^(2) - (l_(1)^(2))/(4)) = sqrt([l_(2)(1 + alphat)]^(2) - (1)/(4)[l_(1)(1 + alphat)]^(2))`
and `l_(1) = l_(2)`