JEE Main201912 Apr 2019Evening ShiftPhysicsThermal Properties of MatterActual
A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of Elasticity equals Y . When this rod is heated by temperature T and simultaneously subjected to a net longutudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to:
Options
- AF / 3 π r 2 Y T
- B9 F / π r 2 Y T
- C6 F / π r 2 Y T
- D3 F / ( π r 2 Y T )
Correct answer
D. 3 F / ( π r 2 Y T )
Step-by-step solution
Stress = F A Y α T = F A α = F A Y T γ = 3 α = 3 F A Y T γ = 3 F π r 2 Y T