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Standard XII

Physics

Energy

The area of c...

Question

The area of cross-section of a railway track is $0.01 m^{2}$ . The temperature variation is $10^{\circ} C$ . Coefficient of linear expansion of material of track is $10^{- 5} /^{\circ} C$ . The energy stored per meter in the track is ${Jm}^{- 1}$ . (Young's modulus of material of track is $10^{11} {Nm}^{- 2})$

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Solution

Elastic energy stored in the track $= \frac{Y}{2} (strain)^{2} \times$ Area $\times$ length

$\Rightarrow Elastic energy per unit length (E) = \frac{Y}{2} (strain)^{2} \times Area$

Here, $(strain = \frac{Δ l}{l} = α Δ T = 10^{- 5} \times 10 = 10^{- 4})$

$\Rightarrow E = \frac{10^{11}}{2} \times (10^{- 4})^{2} \times 10^{- 2} = 5 {Jm}^{- 1}$

Correct answer: $5$

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The area of cross-section of a railway track is 0.01 m2 . The temperature variation is 10 ∘C. Coefficient of linear expansion of material of track is 10−5 /∘C. The energy stored per meter in the track is Jm−1. (Young's modulus of material of track is 1011 Nm−2)

Elastic energy stored in the track=Y2(strain)2× Area × length ⇒Elastic energy per unit length(E)=Y2(strain)2×Area Here, (strain=Δll=αΔT=10−5×10=10−4) ⇒E=10112×(10−4)2×10−2=5 Jm−1 Correct answer: 5