An insect crawls up a hemispherical surface very slowly. The...

The insect crawls up the bowl upto a certain height $h$ only till the component of its weight along the bowl is balanced by limiting frictional force. For limiting condition at point $\mathrm{A} R=m g \cos \alpha F_1=m g \sin \alpha$ Dividing eq. (ii) by (i) $\tan \alpha=\frac{1}{\cot \alpha}=\frac{F_1}{R}=\mu\left[\right.$ As \left.F_1=\mu R\right] \Rightarrow \quad \tan \alpha=\mu=\frac{1}{3}\left[\because \mu=\frac{1}{3}(\right.$Given \left.]\right) \therefore \quad \cot \alpha=3$