The figure below shows an isosceles triangular frame ABC made out of two different materials and D is the midpoint of the side AB. The coefficient of thermal expansion of the rod ADB is `alpha_(1)` and for the rods AC and BC is `alpha_(2)`. End C is fixed and the whole system is placed on a smooth horizontal surface. When the temperature of the system increases, it is found that the distance remains fixed, then

Options

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