a solid hemisphere of weight W rests in limiting equilibrium with its curved surface on a rough inclined plane and its plane face is kept horizontal by a weight W1 attached to a point in its rim. prove that the coefficient of friction is W1/√(W(W+2W1))

Answer 1

If you're still curious:

The equations we get by demanding 0 net force and torque are :

(W1 + W2 )*cosx = N
(W1 + W2 )*sinx = uN
W2 = uN

This tells us that equilibrium can only be achieved at a particular angle of inclination x= arcsin(w2/w1+w2)
Solving these equations further gives us u as the desired result