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  4. A wire elongates by l mm when a load w is hanged from it. If the wire goes over a pulley and two weights w each are hung at the two ends, the elongation of the wire will be (in mm):

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Q. A wire elongates by $ l \,mm$ when a load w is hanged from it. If the wire goes over a pulley and two weights w each are hung at the two ends, the elongation of the wire will be (in mm):

Bihar CECEBihar CECE 2004Mechanical Properties of Solids

Solution:

Let us consider the length of wire as $L$ and cross-sectional area $A$, the material of wire has Young's modulus as $Y$.
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Then for $1\,st$ case, $Y=\frac{w / A}{V L}$
For $2\,nd$ case, $Y=\frac{w / A}{2 l^{'} / L}$
$\therefore l^{'}=\frac{l}{2}$
So, total elongation of both sides $=2 l^{'}=l$