Thermal Properties of Matter

JEE Main level, single correct, medium

37 of 126

Question 37 of 126

A uniform cylindrical rod of length LL and radius r, is made from a material whose Young’s modulus of Elasticity equals Y.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:

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Answer: (D) 3F/(πr2YT)3F/(\pi {r}^{2}YT)

Stress =FA=\dfrac{F}{A}
Y(αT)=FAY\left(\alpha T\right)=\dfrac{F}{A}
α=FA(YT)\alpha =\dfrac{F}{A\left(YT\right)}
γ=3α=3FAYT\gamma =3\alpha =\dfrac{3F}{AYT}
γ=3Fπr2YT\gamma =\dfrac{3F}{\pi {r}^{2}YT}

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