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:

Question

TuteeHUB · Accepted Answer

$\frac{{\rm{F}}}{{\left( {3{\rm{\pi }}{{\rm{r}}^2}{\rm{YT}}} \right)}}$

TuteeHUB · Answer

$\frac{{9{\rm{F}}}}{{\left( {{\rm{\pi }}{{\rm{r}}^2}{\rm{YT}}} \right)}}$

TuteeHUB · Answer

$\frac{{6{\rm{F}}}}{{\left( {{\rm{\pi }}{{\rm{r}}^2}{\rm{YT}}} \right)}}$

TuteeHUB · Answer

$\frac{{3{\rm{F}}}}{{\left( {{\rm{\pi }}{{\rm{r}}^2}{\rm{YT}}} \right)}}$

1.	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.	\(\frac{{9{\rm{F}}}}{{\left( {{\rm{\pi }}{{\rm{r}}^2}{\rm{YT}}} \right)}}\)
B.	\(\frac{{6{\rm{F}}}}{{\left( {{\rm{\pi }}{{\rm{r}}^2}{\rm{YT}}} \right)}}\)
C.	\(\frac{{3{\rm{F}}}}{{\left( {{\rm{\pi }}{{\rm{r}}^2}{\rm{YT}}} \right)}}\)
D.	\(\frac{{\rm{F}}}{{\left( {3{\rm{\pi }}{{\rm{r}}^2}{\rm{YT}}} \right)}}\)
Answer» D. \(\frac{{\rm{F}}}{{\left( {3{\rm{\pi }}{{\rm{r}}^2}{\rm{YT}}} \right)}}\)

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