The elongation in a metallic rod hinged at one end and rotating in a horizontal plane becomes four times of the initial value. The angular velocity of rotation becomes

-∫T0∆T = ∫0lmldxω2 x  ⇒ T = mlω2x22⇒ Y =FlA∆lδl = FlAYδl = mlω2x22dxAY∆l=∫δl = mω2l3 6AYl   ∆l = ρω2l36Y∆ l ∝ ω2For elongation to become 4 times the final angular speed must beω2 = 2ω1