A uniform metal rod of 2, mm^2 cross section fixed between two walls is heated from 0,^oC to 20,^oC

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8.Mechanical Properties of Solids

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A uniform metal rod of $2\, mm^2$ cross section fixed between two walls is heated from $0\,^oC$ to $20\,^oC$. The coefficient of linear expansion of rod is $12\times10^{-6}/^oC$. Its Young's modulus of elasticity is $10^{11} \,N/m^2$. The energy stored per unit volume of rod will be ....... $J/m^3$

A

$2880$

B

$1500$

C

$5760$

D

$1440$

Solution

Energy per unit volume $=\frac{1}{2} \times \mathrm{Y} \times(\text { strain })^{2}$

$=\frac{1}{2} \times Y \times(\alpha \Delta \theta)^{2}$

$=\frac{1}{2} \times 10^{11} \times\left(12 \times 10^{-6} \times 20\right)^{2}=2880 \mathrm{J} / \mathrm{m}^{3}$

Standard 11

Physics

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