question_answer

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 \[1.0\times {{10}^{11}}{{\operatorname{Nm}}^{-2}}\] and \[2.0\times {{10}^{11}}\,N{{m}^{-2}}\], the total extension of the composite wire is:    [JEE ONLINE 23-04-2013]

A)  1.75 mm         

B)       2.0 mm           

C)  1.50mm          

D)       1.25 mm

Correct Answer: D Solution : [d] \[{{Y}_{c}}\times (\Delta {{L}_{c}}/{{L}_{c}})={{Y}_{s}}\times (\Delta {{L}_{s}}/{{L}_{s}})\]

\[\Rightarrow \,1\times {{10}^{11}}\,\times \,\left( \frac{1\times {{10}^{-3}}}{1} \right)\,=2\times {{10}^{11}}\,\times \left( \frac{\Delta {{L}_{s}}}{0.5} \right)\]

\[\therefore \]\[\Delta {{L}_{s}}=\frac{0.5\times {{10}^{-3}}}{2}=0.25mm\]

Therefore, total extension of the composite wire

\[=\Delta {{L}_{c}}+\Delta {{L}_{s}}\]

\[=1\,mm+0.25m=1.25m\]