A copper wire of length 1.0 m and a steel wire of length 0.5 m having… | JEE Main 2013 (23 Apr, Shift 1)

Q29JEE Main 2013 · 23 APR · SHIFT 1Medium

Wire Combinations & Special Cases

A copper wire of length 1.0 m and a steel wire of length 0.5 m having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by 1 mm. If the Young's moduli of copper and steel are respectively $1.0 \times 10^{11}$ Nm ${}^{-2}$ and $2.0 \times 10^{11}$ Nm ${}^{-2}$ , the total extension of the composite wire is:

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Answer: (d)

Same force and area: $\Delta l \propto \frac{L}{Y}$
$\frac{\Delta l_s}{\Delta l_c} = \frac{0.5}{1.0} \times \frac{1.0 \times 10^{11}}{2.0 \times 10^{11}} = \frac{1}{4} \Rightarrow \Delta l_s = 0.25\text{ mm}$
Total $= 1 + 0.25 = 1.25\text{ mm}$ , so the answer is (d).

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Wire Combinations & Special Cases question from JEE Main 2013 (23 Apr, Shift 1)

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