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A uniform cylindrical rod of length L an...

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 longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to:

A

`F//(3pi r^2 YT)`

B

`3F//(pi r^2 YT)`

C

`6 F //(pi r^2YT`

D

`9F // (pi r^2 YT)`

Text Solution

Verified by Experts

The correct Answer is:
B
`sigma = F/A`
`Y alpha T=(F)/(pi r^2)`
`alpha=(F)/(YT pi r^2)`
`gamma =3 alpha =(3F)/(YT pi r^2)`
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