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Q.

A uniform metal rod of 2.2mm² cross-section is heated from $0^{\circ} C$ to $20^{\circ} C$ . The coefficient of the linear expansion of the rod is $12 \times 10^{- 6} /^{0} C$ . Its Young’s modulus of elasticity is $10^{11} {Nm}^{- 2}$ . The energy stored per unit volume of the rod is

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a

$1440 {Jm}^{- 3}$

b

$15750 {Jm}^{- 3}$

c

$1500 {Jm}^{- 3}$

d

$2880 {Jm}^{- 3}$

answer is D.

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Detailed Solution

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Energy stored per unit volume is given by

$u = \frac{Y \times (strain)^{2}}{2} = \frac{10^{11}}{2} \times {(\frac{change in length}{original length})}^{2} Where Y is Young's modulus$

$\Rightarrow u = \frac{10^{11}}{2} {(\frac{αLΔθ}{L})}^{2} = \frac{10^{11}}{2} {(12 \times 10^{- 6} \times 20)}^{2} = 2880 - {Jm}^{- 3}$

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A uniform metal rod of 2.2mm2 cross-section is heated from 0∘C to 20∘C . The coefficient of the linear expansion of the rod is 12×10-6/ 0C . Its Young’s modulus of elasticity is 1011Nm-2 . The energy stored per unit volume of the rod is