A steel wire of 4.0 m is stretched through 2.0 mm. The cross - sectional area of the wire is `2.0 mm^2.` If young's modulus of steel is `2.0 xx10^(11) Nm^(-2)` find (i) the energy density of the wire, (ii) the elastic potential energy stored in the wire.

Options

A. `0.3 J`
B. `0.4 KJ`
C. zero
D. `oo`

Answer

A

Explanation

It I s given that I= 4m,
`Delta I=2xx10^(-3),m A=2xx10^(-6) m^(2)`,
and `Y=2xx10^(11)N//m^(2)`
Energy density of stretched wire
`=(1)/(2)xx "stress"xx"strain"`
`(1)/(2)xxYxx("strain")^(2)`
`=(1)/(2)xx2xx10^(11)xx((2xx10^(-3))/(4))`
`=0.25xx10^(5)J//m^(3)`
`:.` Elastic potential energy = energy density `xx` volume
`=2.5xx10^(4)xx2xx10^(-6)xx4=0.2J`