Find the coefficient of friction.
Classical Mechanics
Level
3
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 -
Q/root(P(Q+2P))
P-Q/root(P(+2Q))
P+Q/root(P(P+2Q))
Q/root(P(P+2Q))
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1 solution
Draw the free body diagram. At the point where the hemisphere is touching the plane- P(Rsin thita)=Q(1-sin thita)R {where thita is the angle of friction}. sin thita=Q/(P+Q) so coefficient of friction=tan thita=Q/root(P(P+2Q))