In an experiment, brass and steel wires of length 1 m each with areas of cross section 1 m m 2 are used. The wires are connected in series and one end of the combined wire is connected to a rigid supp

Question

In an experiment, brass and steel wires of length $1 m$ each with areas of cross section $1 m m^{2}$ 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 $0.2 m m$ is,
[Given, the Young's Modulus for steel and brass are, respectively, $120 \times 10^{9} N / m^{2}$ and $60 \times 10^{9} N / m^{2}$ ]

TestHub · Accepted Answer

Stress will be same in both rods
Stress $= Y_{1} \frac{Δ l_{1}}{l} = Y_{2} \frac{Δ l_{2}}{l}$ … (1)
And
$Δ l_{1} + Δ l_{2} = 0.2 \times 10^{- 3} m$ … (2)
From equation (1) and (2)
Stress $\times (\frac{l}{Y_{1}} + \frac{l}{Y_{2}}) = 0 .2 \times 10^{- 3} m$
Stress $\times (\frac{1}{120 \times 10^{9}} + \frac{1}{60 \times 10^{9}}) = 0.2 \times 10^{- 3} m$
Stress $= 8 \times 10^{6} N / m^{2}$

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