In an experiment, brass and steel wires of length \(1\,m\) each with areas of cross section \(1\,mm^2\) are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress requires to produced a new elongation of \(0.2\,mm\) is [Given, the Young’s Modulus for steel and brass are respectively \(120\times 10^9\,N/m^2\) and \(60\times 10^9\,N/m^2\) ]

\(A = {10^{ - 6}}{M^2}\)

\(stress = \frac{F}{A}\)             \({Y_s} = 120 \times {10^9}\)

\(Stress = \frac{{Stress}}{Y}\)

\(\Delta \ell  = \frac{{\ell  \times F}}{{AY}}\)

\(\Delta {\ell _1} + \Delta {\ell _2} = \frac{{{\ell _1}F}}{{A{Y_1}}} + \frac{{{\ell _2}F}}{{A{Y_2}}} = 0.2 \times {10^{ - 3}}\)

\(\frac{F}{A} = \frac{{0.2 \times {{10}^{ - 3}}}}{{\frac{\ell }{{{Y_1}}} + \frac{\ell }{{{Y_2}}}}}\)

\( = \frac{{0.2 \times {{10}^{ - 3}}}}{{\frac{1}{{120 \times {{10}^9}}} + \frac{1}{{60 \times {{10}^9}}}}} = \frac{{0.2 \times {{10}^{ - 3}} \times {{10}^9} \times 120}}{{1 + 2}}\)

\( = \frac{{0.2 \times {{10}^6} \times 120}}{3} = 8 \times {10^6}\)