JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Elasticity & SHM

The area of cross - section of a railway track is

0.01 m^{2}

. The temperature variation is

1 0^{\circ} C

, Coefficient of liner expansion of material of track is

1 0^{- 5} /^{\circ} C

. The energy stored per meter in the track is ______

J / m

.
(Young's modulus of material of track is

1 0^{11} Nm^{- 2}

)

Answer: 5

Solution

The track is held at fixed length, so the thermal expansion that would have occurred appears instead as elastic strain of the same magnitude:

ε = α Δ T = 1 0^{- 5} \times 10 = 1 0^{- 4}

The elastic energy stored per unit volume is

u = \frac{1}{2} Y ε^{2} = \frac{1}{2} \times 1 0^{11} \times (1 0^{- 4})^{2} = 500 J m^{- 3}

One metre of track has volume

A \times 1 m = 0.01 m^{3}

, so

u A = 500 \times 0.01

The track stores

5

J per metre of its length.

JEE Main · 2021 · 22 Jul 2021 · Shift 2 · Integer answer