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 modulii of copper and steel are respectively \(1.0\times10^{11}\, Nm^{-2}\) and \(2.0\times10^{11}\, Nm^{- 2}\), the total extension of the composite wire is ........ \(mm\)

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Answer & Solution

Correct Answer

(D) \(1.25\)

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Detailed explanation

\({Y_c} \times \left( {\Delta {L_c}/{L_c}} \right) = {Y_s} \times \left( {\Delta {L_s}/{L_s}} \right)\)

\( \Rightarrow 1 \times {10^{11}} \times \left( {\frac{{1 \times {{10}^{ - 3}}}}{1}} \right) = 2 \times {10^{11}} \times \left( {\frac{{\Delta {L_s}}}{{0.5}}} \right)\)

\(\therefore \Delta {L_s} = \frac{{0.5 \times {{10}^{ - 3}}}}{2} = 0.25\,mm\)

Therefore, total extension of the composite

\(wire = \Delta {L_c} + \Delta {L_s}\)

\( = 1\,mm + 0.25\,m = 1.25\,m\)

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Match List\(-I\) with List\(-II.\)

List\(-I\)	List\(-II\)
\((a)\) Magnetic Induction	\((i)\) \({ML}^{2} {T}^{-2} {A}^{-1}\)
\((b)\) Magnetic Flux	\((ii)\) \({M}^{0} {L}^{-1} {A}\)
\((c)\) Magnetic Permeability	\((iii)\) \({MT}^{-2} {A}^{-1}\)
\((d)\) Magnetization	\((iv)\) \({MLT}^{-2} {A}^{-2}\)

Choose the most appropriate answer from the options given below:

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