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):

A) \[l\]                                       

B)        2\[l\]

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 Youngs modulus as Y.     Then for 1 st case, \[Y=\frac{w/A}{l/L}\]                 \[Y=\frac{w/A}{2l/L}\]                 \[\therefore \]  \[l=\frac{l}{2}\] So, total elongation of both sides \[=2l=l\]