Question

A wire of length L is suspended in a vertical plane from a rigid support. A load w is attached to its free end. The increase in length of wire is l . The same wire now passes over a fixed pulley and weight w is attached to each free end of the wire. The total increase in length of wire is

(a) l 

(b) 2l 

(c) 2/l 

(d) 4l

Answer 1

(a) l

Let Y be the Young’s modulus of wire. Then

l = w x L/aY .....(1)

When wire passes over pulley and load w is attached to either end; the length of each part of wire is L/2.

Let l' be increase in length of one part due to applied load w at its free end. Then

∴ Total increase in length of wire = 2' L = L