Question

A body is strained within elastic limits .Show that work done , in the process is 1/2 x stress x strain .

Answer 1

Here is you answer.

Whenever a material is loaded within elastic limit, stress is strain. ... The energy stored in a body, when strained within elastic limit is known as strain energy. B. The maximum strain energy which can be stored in a body is termed as proof resilience.so according to you question

We know that

Y = longitudinalstresslongitudinalstrain

=FA×Lx

stress = xL

strain= FA

w=∫dw=∫F.dx

=∫Y.A.xL.dx

YA/L Fxdx

1/2 into x into yax/L

1/2 into x into F

Work/Volume=1/2 into F/A into x/L

1/2 into stress into strain

hence proved.In the above into means multiplication.I was not gettin its sign so i wrote into instead of sign.

Hope it works!