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 $\frac{m a}{n b^{2} c} .$ Find $(m+n)$

Answer 1

$T_{s}=3\, m g$
$\frac{3 m g}{A_{s}}=Y_{s} \times \frac{\Delta l_{s}}{l_{s}}$
$\frac{2 m g}{A_{b}}=Y_{b} \times \frac{\Delta l_{b}}{l_{b}}$
$\frac{\Delta l_{s}}{\Delta l_{b}}=\frac{3}{2} \times \frac{l_{s}}{l_{b}} \times \frac{A_{b}}{A_{s}} \times \frac{Y_{b}}{Y_{s}}=\frac{3}{2} \times \frac{a}{b^{2} c}$