a
\(\begin{array}{l}
The\,{\rm{insect}}\,crawls\,up\,the\,bowl\,upto\,a\\
certain\,height\,h\,only\,till\,the\,component\\
of\,its\,weight\,along\,the\,bowl\,is\,balanced\,\\
by\,{\rm{limiting}}\,frictional\,force\\
For\,li\,miting\,condition\,at\,{\rm{point}}\,A\\
R = mg\,\cos \alpha \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)\\
{F_1} = mg\,\sin \alpha \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)
\end{array}\)

\(\begin{array}{l}
Dividing\,eq.\,\left( {ii} \right)\,by\,\left( i \right)\\
\tan \,\alpha \, = \frac{1}{{\cot \,\alpha }} = \frac{{{F_1}}}{R} = \mu \left[ {As\,{F_1} = \mu R} \right]\\
 \Rightarrow \,\tan \alpha \, = \mu  = \frac{1}{3}\left[ {\mu  = \frac{1}{3}\left( {given} \right)} \right]\\
\therefore \,\,\cot \alpha \, = 3
\end{array}\)