A solid hemisphere of weight $P$ rests with its curved surface in contact with a rough inclined plane. A weight $Q$ is placed at some point on the rim of the hemisphere to keep its plane surface horizontal then its minimum coefficient of friction is
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At $O$
$\mathrm{P}(\mathrm{R} \sin \phi)=\mathrm{Q}(1-\sin \phi) \mathrm{R}$
$\sin \phi=Q /(P+Q)$
$\mu=\tan \phi=\frac{\mathrm{Q}}{\sqrt{\mathrm{P}(\mathrm{P}+2 \mathrm{Q})}}$
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