# Insect in a bowl

There is a hemispherical bowl with centre O on a table inside which, there is an insect. The bug (which is quite desperate to get out) starts climbing the wall of the vessel. If the coefficient of friction between the surface of the bowl and that of the insect is $$\frac{1}{3}$$, then the maximum inclination $$\theta$$ of OB with the vertical is given by-

×