The area of cross section of a railway track is 0.01 m² jee main 2021

Question

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 _______ J/m.

(Young's modulus of material of track is 10¹¹ Nm^–2 )

Answer 1

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

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

Here, (strain = \(\frac {\triangle I}{I}=\alpha \triangle T = 10 ^ {-5} \times 10 = 10 ^ {-4}\)

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