Question

If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are $a,b$ and $c$, respectively, then the corresponding ratio of increase in their lengths is $\frac{ma}{n{b}^{2}c}.$ Find $(m+n)$

Answer 1

Answer: 5

$T_s=3mg$
$\frac{3mg}{A_s}=Y_s\times \frac{\Delta l_s}{l_s}$
$\frac{2mg}{A_b}=Y_b\times \frac{\Delta l_b}{l_b}$
$\frac{\Delta l_s}{\Delta l_b}=\frac{3}{2}\times \frac{l_s}{l_b}\times \frac{A_b}{A_s}\times \frac{Y_b}{Y_s}=\frac{3}{2}\times \frac{a}{b^{2}c}$