Question

A mass of 2kg is attached to the end of a vertical wire of length 2m and diameter 2mm extend the wire by 1mm. Calculate the young modulus of the wire

Answer 1

The applied load =F=mg=2×9.8=19.6N
diameter =1mm=1×10
−3
m
=> radius=0.5×10
−7
m
Area , A=3.14r
2
=3.14×0.25×10
−6

=0.785×10
−6

We know that,
stress=Force/area
=19.6/0.785×10
−6

24.96×10
−6

change in length,ΔL=1mm=10
−3
m
Length,L=3m
hencestrain=ΔL/L
=10
−3
/3
we know that young's modulus is given by the ratio of stress and strain,
Hence,
E=24.96×10
−6
/10
−3
/3
=74.8×10
9

=7.48×10
10
Nm
−2