A wire of resistance $12\Omega m^{-1}$ is bent to form a complete circle of radius 10 cm. The resistance between its two diametrically opposite point s, A and B, as shown in the figure, is

Circumference of circle $2\times \mathrm{\pi }\frac{10}{100}=\frac{2\mathrm{\pi }}{10}=\frac{\mathrm{\pi }}{5}$

Resistance of wire $=12\times \frac{\mathrm{\pi }}{5}=\frac{12\mathrm{\pi }}{5}$

Resistance of each section $=\frac{12\mathrm{\pi }}{10}\mathrm{\Omega }$

$\therefore$   Equivalent resistance

${\mathrm{R}}_{\mathrm{eq}}=\frac{\frac{12\mathrm{\pi }}{10}\times \frac{12\mathrm{\pi }}{10}}{\frac{12\mathrm{\pi }}{10}+\frac{12\mathrm{\pi }}{10}}=\frac{6\mathrm{\pi }}{10}=0.6\mathrm{\pi }\mathrm{\Omega }$