Q

# Tell me? 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,

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 :

• Option 1)

$9F/(\pi r^{2}YT)$

• Option 2)

$6F/(\pi r^{2}YT)$

• Option 3)

$3F/(\pi r^{2}YT)$

• Option 4)

$F/(3\pi r^{2}YT)$

Views

Coefficient of Linear Expansion -

$\alpha=\frac{\Delta L}{L_{0}\Delta T}$

- wherein

Unit of $\alpha$ is C-1 or  K-1

$Y\alpha T=\frac{F}{\pi r^{2}}$

$\alpha =\frac{F}{\pi r^{2}YT}$

$\wp =3\alpha$

$\wp =\frac{3F}{\pi r^{2}YT}$

Option 1)

$9F/(\pi r^{2}YT)$

Option 2)

$6F/(\pi r^{2}YT)$

Option 3)

$3F/(\pi r^{2}YT)$

Option 4)

$F/(3\pi r^{2}YT)$

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