The increase in energy of a metal bar of length L and cross-sectional area A when compressed with a load M along its length is (where, Y= Young's modulus of the material of metal bar)

Options

A. `(FL)/(2AY)`
B. `(F^(2)L)/(2AY)`
C. `(FL)/(AY)`
D. `(F^(2)L^(2))/(2AY)`

Answer

B

Explanation

Energy `=(1)/(2)xx` stress `xx` strain `xx` volume
`=(1)/(2)(("stress)^(2))/(Y)xx` volume
`=(1)/(2)(((F)/(A))^(2))/(Y)xxL.A["as stress"=(F)/(A),"volume"=lxxA]`
or energy `(E)=(F^(2)L)/(2AY)`