Two wires of same material having radius in ratio 2 : 1 and lengths in ratio 1 : 2. If same force is applied on them, then ratio of their change in length will be

Given, ratio of radius of two wires, r1r2=21and ratio in their lengths,  l1l2=12We know that, Young's modulus,Y=FlAΔl⇒ Δl=FlAYΔl∝lAWhen same force is applied on them, then ratio of change in their lengths,Δl1Δl2=l1A1/l2A2=l1A2l2A1⇒ Δl1Δl2=l1l2⋅r22r12=12⋅122=18