Two copper wires have length in the ratio 2:3, area of cross section in the ratio $3: 2$. If they ar

Question

Two copper wires have length in the ratio 2:3, area of cross section in the ratio $3: 2$. If they are applied by same force, the ratio of change in length is

Professor PC Thomas Classes · Answer

Change in length $\Delta L = \frac{FL}{AY} \implies \Delta L \propto \frac{L}{A}$. So, $\frac{\Delta L_1}{\Delta L_2} = \left(\frac{L_1}{L_2}ight) 	imes \left(\frac{A_2}{A_1}ight) = \left(\frac{2}{3}ight) 	imes \left(\frac{2}{3}ight) = \frac{4}{9}$. Ratio is $4:9$.