Question

Relation between volume strain and longitudinal strain

Answer 1

longitudinal strain =change in length/ original length =dl/l
volume strain = change in volume / original volume = dv/v
v =l^3
dv =d(l^3)=3l^2×dl
dv/v = 3 l^2 dl/v =3l^2×dl/l^3 =3 dl/l
volume strain = 3× longitudinal strain

Answer 2

Longitudinal strain =change in length/ original length =dl/l

volume strain = change in volume / original volume = dv/v

v =l^3

dv =d(l^3)=3l^2×dl

dv/v = 3 l^2 dl/v =3l^2×dl/l^3 =3 dl/l

volume strain = 3× longitudinal strain