A cable breaks if stretched by more than 2mm.it is cut into 2 equal parts.how much either part can be stretched without breaking?

1 Answer

#1\ mm#

Explanation:

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#