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)

The situation is shown in fig let L and A be the length and area of cross-section of the wire respectively.For first case,Y=W/Al/L……………..(1)where Y is young's modulus of the material of the wire. If l 'be the elongation in the wire in second case, thenY=W/A2l′/L……………………………(2)From equations (1) and (2), we getW/Al/L=W/A2l′/L or , l=2l′  or  l′=l/2So, total elongation of both sides =2l′=l