A uniform cylindrical rod of length $\mathrm{L}$ 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 longitudinal compressional force $\mathrm{F}$, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to:

Question:

A uniform cylindrical rod of length $\mathrm{L}$ 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 longitudinal compressional force $\mathrm{F}$, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to:

1. $9 \mathrm{~F} /\left(\pi r^{2} \mathrm{YT}\right)$

2. $6 \mathrm{~F} /\left(\pi r^{2} \mathrm{YT}\right.$

3. $3 \mathrm{~F} /\left(\pi r^{2} \mathrm{YT}\right)$

4. $\mathrm{F} /\left(3 \pi r^{2} \mathrm{YT}\right)$

JEE Main Previous Year Single Correct Question of JEE Main from Physics Mechanical Properties of Solids chapter.

JEE Main Previous Year 12 April 2019

Correct Option: 3

Solution: