The area of cross-section of railway track is `0.01m^(2)`. The temperature variation is `10^(@)C`. Coefficient of linear expansion of stell `=10^(-5)//^(@)C`, Young's modulus of steel `=10^(11)Nm^(-2)`. The energy stored per meter in the track is

Options

A. `5J`
B. `10J`
C. `15J`
D. `20J`

Answer

A

Explanation

Let `alpha=` coefficient of linear expansion
`:.` Elastic energy `=(1)/(2)xx` Stress `xx`Strain `xx` Volume
or `U=(1)/(2)xx(Yxx"strain")xx` strain `xx` volume or `U=(1xxYxx("strain")^(2)xx"Volume")/(2)`
`alpha=(l)/(Lxxt)=("strain")/(t)`
`:.alpha=("Change in length")/("Original length"xx"temperature length")` or strain `=alphat`
`:.U=(Yxxalpha^(2)t^(2)xx("Area"xx"length"))/(2)` or `U=(10^(11)xx(10^(-5))^(2)xx(10)^(2)xx0.01xx1)/(2)=5J`
`:.` Energy stored `=5J`