Question

If the ratio of diameters, lengths and Young's modulus of steel and copper wires shown in the figure are p,q, and s respectively, then the corresponding ratio of increase in their lengths would be ____.

Answer 1

$\frac{d_s}{d_c}=p$

$\frac{r_s}{r_c}=p$

$\frac{l_s}{l_c}=q$

$\frac{Y_s}{Y_c}=s$

$F_s=\frac{Y_s{A}_s}{l_s}.(\Delta l{)}_s=7mg$

$F_c=5mg$

$\frac{F_s}{F_c}=\frac{7}{5}$

$\frac{Y_s{A}_s.(\Delta l{)}_s{l}_c}{l_s{Y}_c{A}_c(\Delta l{)}_c}=\frac{7}{5}$

$\left(\frac{Y_s}{Y_c}\right).\left(\frac{A_s}{A_c}\right).\left(\frac{l_c}{l_s}\right).\left[\frac{(\Delta l{)}_s}{(\Delta l{)}_c}\right]=\frac{7}{5}$

$s.p^2\frac{1}{q}\frac{(\Delta l{)}_s}{(\Delta l{)}_c}=\frac{7}{5}$

$\frac{(\Delta l{)}_s}{(\Delta l{)}_c}=\frac{7q}{5p^{2}s}$