Question

Two wires of equal cross section but one made of steel and the other of copper are joined end to end. When the combination is kept under tension, the elongations in the two wires are found to be equal. Find the ratio of the lengths of the two wires. Young modulus of steel = 2.0 x 10¹¹ N m^-2 and that of copper = 1.1 x 10¹¹ N m^-2.

• A. $L_c=\frac{11}{20}$
• B. $\frac{L_s}{L_c}=\frac{20}{11}$
• C. $\frac{L_s}{L_c}=\frac{19}{21}$
• D. $\frac{L_s}{L_c}=\frac{21}{25}$

Answer 1

The correct option is B

$\frac{L_s}{L_c}=\frac{20}{11}$

As the cross sections of the wires are equal and same tension exists in both, the stresses developed are equal. Let the original lengths of the steel wire and the copper wire be$L_S$ and $L_C$ respectively and the elongation in each wire be l.

$\frac{l}{L_s}=\frac{stress}{2.0\times {10}^{11}N{m}^{-2}}.....\left(i\right)$
$\frac{l}{L_c}=\frac{stress}{1.1\times {10}^{11}N{m}^{-2}}.....\left(ii\right)$

Dividing (ii) by (i)
$\frac{L_s}{L_c}=\frac{2.0}{1.1}=20:11$