Question

Two exactly similar wires of steel (y$=$20 x 10${}^{11}$dyne/cm${}^2$) and copper (y $=$ 12 x 10${}^{11}$ dyne/cm${}^2$)are stretched by equal forces. If the total elongation is 1cm, elongation of copper wire is

• A. $3/5cm$
• B. $5/3cm$
• C. $3/8cm$
• D. $5/8cm$

Answer 1

The correct option is D $5/8cm$

$△l=\frac{Fl}{AY}$

$△l_s=\frac{Fl}{A{Y}_s}-1$ (different cases have different subscripts)

$△l_c=\frac{Fl}{A{Y}_c}-2$

Dividing 1 and 2

$\frac{△l_s}{△l_c}=\frac{Y_c}{Y_s}=\frac{12\times {10}^{11}}{20\times {10}^{11}}=\frac{3}{5}$

$1cm=△l_s+△l_c$

$1cm=\frac{3}{5}△l_c+△l_c$

$1cm=\frac{8}{5}△l_c$

$So,△l_c=\frac{5}{8}cm$