Three rods of equal of length are joined to from an equilateral triangle ABC. `D` is the midpoint of AB. The coefficient of linear expansion is `alpha_(1)` for AB and `alpha_(2)` for `AC` and `BC` . If the distance `DC` remains constant for small changes in temperature,

Options

A. (a)`alpha_(1) = alpha_(2)`
B. (b)`alpha_(1) = 2alpha_(2)`
C. (c)`alpha_(1) = 4alpha_(2)`
D. (d)`alpha_(1) =(1)/(2)alpha_(2)`

Answer

C

Explanation

`DC^(2) = L_(2)^(2) - (L_(1)^(2))/(4) implies 0 = 2L_(2) DeltaL_(2) - (2L_(1) DeltaL_(1))/(4)`
`implies 0 = 2L_(2)(alpha_(2)L_(2)theta) - (2L_(1)(alpha_(1)L_(1)theta))/(4) implies alpha_(1) = 4alpha_(2)`