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

Options

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

Answer

A

Explanation

Let `alpha ` = coefficient of linear expansioin .
`:.` Elastic energy `=(1)/(2) xx (Y xx "strain") xx "strain" xx "volume " ` or `U = (1xx Y xx ("strain")^(2) xx "Volume")/(2)`
`alpha= (l)/(L xx t) = ("strain")/(t)`
`because alpha= ("Change in length ")/("Original length " xx"temperature length")` or strain = at
`:. U= (Yxx alpha^(2) t^(2) xx ("Area" xx "length"))/(2) " or" U = (10^(11) xx (10^(-5))^(2) xx (10)^(2) xx 0.01 xx 1)/(2) = 5 J`
`:.` Energy stored =5 J