Question

Two wires are made of the same material and have the same volume. However, wire 1 has cross- sectional area A and wire-2 has cross-sectional area 3A. If the length of wire 1 increases by Ax on applying force F, how much force is needed to stretch wire 2 by the same amount?

Answer 1

Since the two wires have same volume.Length of wire 1 $=l$Length of wire 2 $=\large\frac{l}{3}$Area of wire 1 $=A$Area of wire 2 $=3A$wire 1:$Y=\large\frac{F/A}{\Delta x /l}$---------(1)wire 2:$Y=\large\frac{F'/A}{\Delta x /l/3}$-------------(2)from (1) and (2)$\large\frac{F}{A} \times \frac{l}{\Delta x}=\frac{F^1}{3A} \times \frac{l}{3 \Delta x}$$F^1=9F$Hence c is the correct answer.