Question

A uniform rod of mass m length L area of cross section A is rotated about an Axis through one of its ends and perpendicular to its length with constant angular velocity w in a horizontal plane. If Y is the Young's modulus of the material of the rod, the increase in its length due to rotation of rod is

Answer 1

Hook’s Law: Stress = Young’s Modulus × strain

⇒F/A=Yδ/L⇒δ=FLAY

dδ=dFxAY

dF= centrifugal force due to mass of the element of length dx

=dMxω2=MLxdxω2

dδ=MLdxω2x.xAY

δ=∫L0Mω2LAYx2dx=Mω2L23AY