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Question:

In an experiment, brass and steel wires of length 1m each with areas of cross section 1mm² are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and the other end is subjected to elongation. The stress required to produce a net elongation of 0.2mm is :(Given, the Young's Modulus for steel and brass are respectively, 120×10⁹N/m and 60×10⁹N/m)

0.2×10⁶N/m

4.0×10⁶N/m

1.8×10⁶N/m

1.2×10⁶N/m

Solution:

Correct option is B. 4.0×10⁶N/m
k₁ = y₁A₁Δl₁ = 120×10⁹ × A₁
k₂ = y₂A₂Δl₂ = 60×10⁹ × A₁
keq = k₁k₂/(k₁ + k₂) = (120 × 60)/(180) × 10⁹ × A
keq = 40 × 10⁹ × A
F = keq(x)
F = (40 × 10⁹)A (0.2 × 10⁻³)
FA = 8 × 10⁶ N/m²
No option is matching. Hence question must be bonus.