In an experiment, brass and steel wires of length 1 m each with areas of cross section $1 \mathrm{~m

Question

In an experiment, brass and steel wires of length 1 m each with areas of cross section $1 \mathrm{~mm}^{2}$ 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 required to produce a net elongation of 0.2 mm is,\ [Given, the Young's Modulus for steel and brass are, respectively, $120 	imes 10^{9} \mathrm{~N} / \mathrm{m}^{2}$ and $60 	imes 10^{9} \mathrm{~N} / \mathrm{m}^{2}$ ]\

Professor PC Thomas Classes · Answer

The Young's modulus of two wires connected in series is\ $Y=\frac{2 Y_{1} Y_{2}}{Y_{1}+Y_{2}}=\frac{2\left(120 	imes 10^{9}ight)\left(60 	imes 10^{9}ight)}{180 	imes 10^{9}}$\ $=80 	imes 10^{9} \mathrm{~N} \mathrm{~m}^{-2}$\ So, the stress required $F=Y 	imes$ strain\ $=80 	imes 10^{9} 	imes \frac{0.2 	imes 10^{-3}}{2}=8.0 	imes 10^{6} \mathrm{~N}$\