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Find minimum height of the obstacle so that the shpere can stay in equilibrium

Find the minimum height of the obstacle so, that the sphere can stay in equilibrium.

Find the minimum height of a mirror where one can see his full image.

Find the minimum height of a mirror where one can see his full image.

The minimum number of non coplanar forces that can keep a particle in equilibrium is

The centre of mass of an inhomogeneous sphere is at a distance of 0.3 R from its geometrical centre. R is the radius of the sphere. Find the maximum inclination (theta) of an incline plane on which this sphere can be placed in equilibrium. Assume that friction is large enough to prevent slipping.