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 Δl 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 = A1 Force applied = F1 and 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=FI1A1ΔI ….(i)For wire 2, Area of cross-section = A2 Force applied = F2 and increase in length =Δl∵ Volume, V=Al or I=VASubstituting the value of I in Eqs. (i) and (ii), we getY1=F1VA12Δl and Y2=F2VA22ΔlIt is given that the wires are made up of same material, i.e.        Y1 =  Y2⇒F1VA12Δ1=F2VA22Δ1⇒F1F2=A12A22=A29A2=19 ∵A1=A and A2=3A or, F2=9F1=9F Given ,F1=F