An insect crawls up a hemispherical surface v | vedclass

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Question

$\begin{array}{l}
The\,{m{insect}}\,crawls\,up\,the\,bowl\,upto\,a\
certain\,height\,h\,only\,till\,the\,component\
of\,its\,weight\,along\,the

Vedclass · Accepted Answer

$\cot \,\alpha  = 3$

Vedclass · Answer

$\begin{array}{l}
The\,{m{insect}}\,crawls\,up\,the\,bowl\,upto\,a\
certain\,height\,h\,only\,till\,the\,component\
of\,its\,weight\,along\,the\,bowl\,is\,balanced\,\
by\,{m{limiting}}\,frictional\,force\
For\,li\,miting\,condition\,at\,{m{point}}\,A\
R = mg\,\cos \alpha \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i ight)\
{F_1} = mg\,\sin \alpha \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} ight)
\end{array}$

$\begin{array}{l}
Dividing\,eq.\,\left( {ii} ight)\,by\,\left( i ight)\
	an \,\alpha \, = \frac{1}{{\cot \,\alpha }} = \frac{{{F_1}}}{R} = \mu \left[ {As\,{F_1} = \mu R} ight]\
 \Rightarrow \,	an \alpha \, = \mu  = \frac{1}{3}\left[ {\mu  = \frac{1}{3}\left( {given} ight)} ight]\
	herefore \,\,\cot \alpha \, = 3
\end{array}$

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