A steel wire 4.0 m in length 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 xx 10^(11) Nm^(-2)`, then find the energy density of wire.

Options

A. `2.5 xx 10^(4) Jm^(-3)`
B. `0.5 xx 10^(4) Jm^(-3)`
C. `1.6 xx 10^(4) Jm^(-3)`
D. `3.6 xx 10^(4) Jm^(-3)`

Explanation

Given, `l = 4.0 m, Delta l = 2 xx 10^(-3) m`
`A = 2.0 xx 10^(6) m^(2)` and `Y = 2.0 xx 10^(11) Nm^(-2)`
The energy density of stretched wire,
`U = (1)/(2) xx` Stress `xx` strain
`U = (1)/(2) xx Y xx ("strain")^(2)`
`= (1)/(2) xx 2.0 xx 10^(11) xx ((2 xx 10^(-3))/(4))^(2)`