Let dl be the change in the length of small element due to rotation by the application of force dF The expression for Young's modulus is given by, Y=
dF∕A
dl∕x
dF=
AYdl
x
⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(I) Now, dF is the centrifugal force due to mass of the element of length dx dF=dm⋅xω2 =
m
L
⋅xdxω2⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(II) From equation (I) and (II),