Correct Answer - Option 1 : 16 megaohm
Concept:
Insulation resistance is inversely proportional to length of the cable
\(R = \frac{\rho }{{2\pi l}}\log \frac{{{r_2}}}{{{r_1}}}\)
\(\Rightarrow R \propto \frac{1}{l}\)
where,
r2 = radius of cable,
r1 = radius of core conductor,
l = length of cable
Calculation:
l1 = 20 km, R1 = 8 MΩ, l2 = 10 km
\(\Rightarrow \frac{{{R_1}}}{{{R_2}}} = \frac{{{l_2}}}{{{l_1}}}\)
\(\Rightarrow \frac{{8 }}{{{R_2}}} = \frac{10}{20} \Rightarrow {R_2} = 16\;M{\rm{Ω }}\)
