The correct option is A 2:√7
From Ohm's law, we know that potential difference V=iR, where i is the current flowing and R is the resistance of the wire given by R=ρlA
ρ is the specific resistance of the material which is a constant in this case as the two wires are of the same material.
A is the area of the cross section of the wire = πr2, r is the radius of the cross section of the wire.
Given, voltages V1=4.2V and V2=3.6V
Ratio of lengths = l1:l2=2:3
We have V∝lr2
⟹r1r2=√V2×l1V1×l2 = √3.6×24.2×3 = 2√7.