Question

Two wires A and B are of same materials. Their lengths are in the ratio 1 : 2 and diameters are in the ratio 2 : 1 when stretched by force F_A and F_B respectively they get equal increase in their lengths. Then the ratio F_A/F_B should be

• A. 1 : 2
• B. 1 : 1
• C. 2 : 1
• D. 8 : 1

Answer 1

Answer: (D)

8 : 1

Answer 2

$Y = \frac{FL}{\pi r^{2}l}$ $\therefore F = Y\pi r^{2}\frac{l}{L}$

$\frac{F_{A}}{F_{B}} = \frac{Y_{A}}{Y_{B}}\left( \frac{r_{A}}{r_{B}} \right)^{2}\left( \frac{l_{A}}{l_{B}} \right)\left( \frac{L_{B}}{L_{A}} \right) = 1 \times \left( \frac{2}{1} \right)^{2} \times (1) \times \left( \frac{2}{1} \right) = 8$