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?

According to the question,For wire 1 Area of cross-section = A1Force applied = F1and increase in length = ΔlFrom the relation of Young's modulus of elasticity,Y=FlAΔlSubstituting the values for wire 1 in the above relation, we get⇒ Y1=Fl1A1Δl         …(i)For wire 2 Area of cross-section = A2Force applied = F2and increase in length = ΔlSimilarly,  Y2=F2l2A2Δl         …(ii)∵  Volume,  V=Al or l=VASubstituting the value of I in Eqs. (i) and (ii), we getY1=F1VA12Δl and Y2=F2VA22Δlis given that the wires are made up of same material, i.e.        Y1 =  Y2⇒ F1VA12Δl=F2VA22Δl⇒ F1F2=A12A22=A29A2=19 ∵A1=A and A2=3Aor,      F2=9F1=9F    (Given, F1 = F)