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