An insect crawls up a hemispherical surface very slowly. The coefficient of friction between insect and surface is $\large\frac{1}{3}$. If the line joining the center of hemispherical surface to the insect makes an angle $\alpha$ with the vertical the maximum possible angle of $\alpha$ is

Question

$ a) \cot \alpha=3 \qquad b)\sec \alpha=3 \qquad c) cosec \alpha=3 \qquad d) none $