Question

Two wires A and B are of same materials. Their length are in the ratio 3 : 4 and diameters are in the ratio $5 : 1$ when stretched by force $F_{A}$ and $F_{B}$ respectively they get equal in increase in their lengths. The ratio of $F_B/F_A$ is.

• A. 0.01
• B. 0.03
• C. 0.04
• D. 0.05

Answer 1

Answer: (B)

$F =\frac{Y A \Delta L}{L}$
$F \propto \frac{r^{2}}{L}$
$\therefore \frac{F_{B}}{F_{A}} =\frac{r_{B}^{2}}{\left(r_{A}\right)^{2}} \times \frac{L_{A}}{L_{B}}=\left(\frac{1}{5}\right)^{2} \times \frac{3}{4}$
$=\frac{3}{4} \times \frac{1}{25}=0.03$