A wire of length $L_{0}$ is supplied heat to raise its temperature by T. If γ is the coefficient of volume expansion of the wire and Y is young's modulus of the wire then the energy density stored in the wire is

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$\frac{1}{2} {γT}^{2} Y$

$\frac{1}{3} γ^{2} T^{2} Y^{3}$

$\frac{1}{18} \frac{γ^{2} T^{2}}{Y}$

$\frac{1}{18} γ^{2} T^{2} Y$

answer is D.

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Detailed Solution

$u_{B} = \frac{1}{2} \times stress x strain = \frac{1}{2} \times Y \times (strain)^{2} = \frac{1}{2} \times Y (αT)^{2} α = γ / 3 = \frac{1}{18} γ^{2} {YT}^{2}$

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