Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by ∆l on applying a force F, how much force is needed to stretch the second wire by the same amount?

Young's modulus, Y=FlAΔlSince initial volume of wires are same Their areas of cross sections are A and 3 A  and lengths are 3l and l respectively.For wire 1,Δl=FAY3l            ...........(i)  For wire 2 , let F' force is applied F'3A=YΔll⇒Δl=F'3AYl         ..........(ii)From the equations (i) and (ii)Δl=FAY3l=F'3AYl⇒F':