Question

If the ratio of lengths, radii and Youngs moduli of steel and brass wires in the figure are $a,b$ and $c$, respectively, then the corresponding is

• A. $\frac{2a^{2}c}{b}$
• B. $\frac{3a}{2b^{2}c}$
• C. $\frac{2ac}{b^2}$
• D. $\frac{3c}{{2ab}^2}$

Answer 1

Answer: (B)

$\frac{3a}{2b^{2}c}$

$T_S=3mg$

$T_B=2mg$
$\frac{3mg}{A_s}=y_s\times \frac{\Delta l_s}{l_s}$
$\frac{2mg}{A_b}=y_b\times \frac{\Delta l_b}{l_b}$
$\frac{\Delta l_s}{\Delta l_b}=\frac{3}{2}\times \frac{l_s}{l_b}\times \frac{A_b}{A_s}\times \frac{y_b}{y_s}=\frac{3}{2}\times \frac{a}{b^{2}c}$