If x longitudinal strain is produced in a wire of Young's modulus Y, then potential energy stored in a material of the wire per unit volume is ..........

Options

A. `Yx ^(2)`
B. `2Yx ^(2)`
C. `(Y^(2) x )/(2)`
D. `(Yx ^(2))/(2)`

Answer

D

Explanation

Potential energy stred in a wire per unit volume
`U =1/2 xx ` stress `xx` strain
`=1/2 xx Yxx` strain `xx` strain `[ because Y= ("Stress")/("Strain") ]`
`= (Yxx ("strain") ^(2))/(2)`
`= (Yx ^(2))/(2)`