question_answer

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)                                                    [AIEEE 2006]

A)  \[l\]                 

B)       \[2l\] C)  zero                  D)       \[l/2\] Correct Answer: A Solution : [a] Let us consider the length of wire as L and cross-sectional area A the material of wire has

Young's modulus as Y.

For 1st case, \[y=\frac{W/A}{l/L}\]\[\left[ \because Y=\frac{stress}{strain}=\frac{F/A}{l/L} \right]\]

For 2nd case, \[Y=\frac{W/A}{2l'/L}\]

\[\therefore \]\[l'=l/2\]

So, total elongation of both sides\[=2l'=l\]