Two metal rods of the same length and area of cross-section are fixed end to end between rigid supports. The materials of the rods have Young module `Y_(1)` and `Y_(2)` , and coefficient of linear expansion `alpha_(1)` and `alpha_(2)` . The junction between the rod does not shift and the rods are cooled

Options

A. `Y_(1)alpha_(1) = Y_(2)alpha_(2)`
B. `Y_(1)alpha_(2) = Y_(2)alpha_(1)`
C. `Y_(1)alpha_(1)^(2) = Y_(2)alpha_(1)^(2)`
D. `Y_(1)^(2)alpha_(1) = Y_(2)^(2)alpha_(2)`

Answer

A

Explanation

`DeltaL = DeltaL_("thermal") - DeltaL_("contact force") = 0 implies alpha_(1)1, theta= (FL)/(AY_(1)) (rod-1`)
`alpha_(2)Ltheta= (FL)/(AY_(2)) (rod-2) implies Y_(1)alpha_(1) = Y_(2)alpha_(2)`