Under the application of force, a steel wire (`Y = 19xx10^10 N m^-2`) of 5 m in length suffers an elongation of 1 mm. The potential energy stored per unit volume in this process, in `J//m^3` is

Options

A. `1.9xx10^3`
B. `9.4xx10^3`
C. `9.5xx10^3`
D. `3.8xx10^3`

Answer

D

Explanation

Potential energy per unit volume
`U= 1/2 xx "stress" xx "strain"`
`=1/2 xx Yxx "strain"^(2)` [`because Y = ("Stress")/("strain")`]
`=1/2 xx 19 xx 10^(10) ((Deltal)/l)^(2)`
`=1/2xx 19 xx 10^(10) ((-10^(-3))/5)^(2)`
`=3.8xx10^(9)xx10^(-6)`
`=3.8xx10^(3) j//m^(3)`