A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of…

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:
  1. F/3πr2YT
  2. 9F/πr2YT
  3. 6F/πr2YT
  4. 3F/(πr2YT)

Solution

Stress =FA
YαT=FA
α=FAYT
γ=3α=3FAYT
γ=3Fπr2YT

Asked in: JEE Main 2019 (12 Apr Shift 2)

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