A wire of length `L_0` is supplied heat to raise its temperature by T. if `gamma` is the coefficient of volume expansion of the wire and Y is Young's modulus of the wire then the energy density stored in the wire is

Options

A. `(1)/(2)gamma^(2)T^(2)Y`
B. `(1)/(3)gamma^(2)T^(2)Y^(3)`
C. `(1)/(18)(gamma^(2)T^(2))/(Y)`
D. `(1)/(18)gamma^(2)T^(2)Y`

Answer

D

Explanation

Elastic potential energy per unit volume
`E = (1)/(2) xx "Stress" xx "Strain" = (1)/(2) xx Y xx ("Strain")^(2)`
`rArr E = (1)/(2) xx Y xx ((DeltaL)/(L))^(2) = (1)/(2) xx Y xx alpha^(2) xx DeltaT^(2)`