Question

Steel and copper wires of same length are
stretched by the same weight one after the
other. Young's modulus of steel and copper
are 2x10" N / m2 and 1.2x10" N / m2. The ratio
of increase in length is?​

Answer 1

Let us take wires of length l,

They are stretched by a weight which produces Stress t in both the wires.

Let the increase in length be e for steel and c for copper.

Young's modulus for steel is given as,

$\gamma = \frac{stress}{strain} \\ \\ 2 \times 10 ^{11} = \frac{ t}{ \frac{e}{l} } \\ \\ 2 \times {10}^{11} = \frac{tl}{e}$

Young's modulus for steel is given as,

$\gamma = \frac{stress}{strain} \\ \\ 1.2\times 10 ^{11} = \frac{ t}{ \frac{c}{l} } \\ \\1. 2 \times {10}^{11} = \frac{tl}{c}$

Now,

Ratio of increase in lengths of steel and copper is,

$e \ratio \: c = \dfrac{ \dfrac{tl}{2 \times {10}^{11} } }{ \dfrac{tl}{1.2 \times {10}^{11} } } \\ \\ e \ratio \: c = \frac{tl}{tl} \times \frac{1.2}{2} \times \frac{ {10}^{11} }{ {10}^{11} } \\ \\ e \ratio \: c = 0.6 \\ \\ e \ratio \: c = \frac{6}{10 } = \frac{3}{5}$

Therefore, The ratio of increase in length is 3 : 5.