c
(c) Let $P$ force is acting at an angle $30^o $ with the horizontal.
For the condition of motion $F = \mu \;R$
$P\cos 30^\circ = \mu \,(mg - P\sin 30^\circ )$
==> $P\frac{{\sqrt 3 }}{2} = \frac{1}{{\sqrt 3 }}\left( {100 - P\frac{1}{2}} \right)$
==>$\frac{{3P}}{2} = \left( {100 - \frac{P}{2}} \right)$
==> $2P = 100$ $\therefore \;\;P = 50\;N$