b
\(\begin{array}{l}
The\,{\rm{maximum}}\,value\,of\,static\,friction\,up\\
to\,which\,body\,does\,not\,move\,is\,called\,\\
{\rm{limiting}}\,friction.\\
\,\,\,\,\,\,\,\,\,Angle\,of\,repose\,is\,defined\,as\,the\,angle\\
\,\,\,\,\,\,\,\,\,\,of\,the\,inclined\,plane\,with\,horizontal\\
\,\,\,\,\,\,\,\,\,\,such\,that\,a\,body\,placed\,on\,it\,is\,just\,\\
\,\,\,\,\,\,\,\,\,\,begins\,to\,slide.\\
\,\,\,\,\,\,\,\,\,In\,{\rm{limiting}}\,{\rm{condition,}}\\
\,\,\,\,\,\,\,\,\,F = mg\sin \alpha \,and\,R = mg\cos \alpha \\
\,\,\,\,\,\,\,\,\,where\,\alpha  - angle\,of\,repose.
\end{array}\)

\(\begin{array}{l}
\,\,So\,\frac{F}{R} = \tan \alpha \\
\,\,\,\,\,\,\,\,\,\,\therefore \frac{F}{R} = {\mu _2} = \tan \theta  = \tan \alpha \,\,\,\left( {\tan \theta  = {\mu _s}} \right)\\
\,\,\,\,\,\,\,\,\,\,or\,\theta  = \alpha \\
\,\,\,\,\,\,\,\,\,\,i.e,.\,angle\,of\,friciton\, = \,angle\,of\,repose.
\end{array}\)