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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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