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  Solved  Paper-2006

A) \[l\]                       

B)        \[2l\]                    

C) zero                      

D)        \[l/2\]

Correct Answer: A

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. 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\[=2l'=l\]