Draw a free body diagram of given problem
Calculate tension in the wire
Let tension in the wire be T,
20−T=2a …(i)
T−20=a …(ii)
Therefore, on solving both equations we get
20−TT−10=2
⇒20−T=2T−20
T=403 N
Calculate area of cross section of the wire
Formula used: σ=TA
As we know,
stress,σ=TA
⇒2×109=40/3A
A=203×10−9m2
Calculate minimum radius of the wire
Let r be the radius of the wire, and area will be equal to πr2 Therefore,
πr2=20×10−9/3
r=(20×10−93×3.14)12
=0.46×10−4 m=46μm