NTA Abhyas JEE Main2020PhysicsThermal Properties of MatterPractice
Two metal rods of the same lengths and area of cross-sections are fixed end to end between rigid supports. The materials of the rods have Young's moduli Y 1 and Y 2 and coefficients of linear expansion are α 1 and α 2 . The junction between the rods does not shift if the rods are cooled. Then
Options
- AY 1 α 1 = Y 2 α 2
- BY 1 α 2 = Y 2 α 1
- CY 1 α 1 2 = Y 2 α 2 2
- DY 1 2 α 1 = Y 2 2 α 2
Correct answer
A. Y 1 α 1 = Y 2 α 2
Step-by-step solution
Here Y 1 and Y 2 are Young's moduli of the material of the rods and α 1  and  α 2 are the coefficients of thermal expansion. Using Y = stress strain , T = Y A α t , where t   is the temperature. Tension must be the same in both the rods for their junction to be in equilibrium. ∴     Y 1 A α 1 t = Y 2 A α 2 t