In general, the elongation #\Delta L# of a metallic cable of young modulus #E#, cross-sectional, area #A# & length #L# under the tensile load P is given as follows
#\Delta L=\frac{PL}{AE}#
#\Delta L\prop L#
Keeping #P, A, E# constant, the elongation #\Delta L# of cable is directly proportional to its length #L#
From above proportionality we have
#\frac{\Delta L_2}{\Delta L_1}=\frac{L_2}{L_1}#
Since, the cable of length #L_1# having elongation #\Delta L_1=2\ mm# is broken into two equal parts so each part has now a length #L_2=L_1/2# i.e. half the original length hence the elongation #\Delta L_2# of each part under same tensile load #P#
#\frac{\Delta L_2}{2}=\frac{L_1/2}{L_1}#
#\frac{\Delta L_2}{2}=1/2#
#\Delta L_2=2/2=1#
hence, each parts is now stretched by #1\ mm#