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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; so that its length remain unchanged. The coefficient of volume expansion of the material of the rod is nearly equal to

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$\frac{6 F}{π r^{2} Y T}$

$\frac{F}{3 π r^{2} Y T}$

$\frac{9 F}{π r^{2} Y T}$

$\frac{3 F}{π r^{2} Y T}$

answer is D.

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Detailed Solution

As length remains same, expansion due to temperature = compression due to longitudinal force.
$L α Δ t = \frac{F L}{A Y}$ $α = \frac{F}{π r^{2} Y T}$

Coefficient of volume expansion of material rod

$= γ = 3 α = \frac{3 F}{π r^{2} Y T}$

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