When an elastic material with Young's modulus Y is subjected to stretching stress S, elastic energy stored per unit volume of the material is :

Options

A. `(YS)/(2)`
B. `(S ^(2)Y)/(2)`
C. `(S ^(2))/(2Y)`
D. `(S)/(2Y)`

Answer

C

Explanation

Energy stored per unit volume
`=1/2 xx ` stress `xx` strain
`=1/2xx` stress `xx (("stress")/("Young.s modulus"))`
`=1//2 xx (("stress") ^(2))/("Young .s modulus") = (S ^(2))/( 2Y)`