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If A particle of mass m resting at the top of a fixed smooth hemisphere of radius R is displaced then the angle with vertical at which it looses contact with the surface is 

Asked by m.nilu 6th September 2018, 11:14 PM
Answered by Expert
Though it is given in the question, surface is smooth, without friction it is not possible to hold a block of mass
on hemi-spherical surface when the line joining the centre of hemisphere and centre of block makes an angle with the vertical line.
So i assume there is friction on the surface.
Figure shows the force and the resolved components of weight of the block.
when μN < ( mg sinθ ) block will not fall. hence the condition for the block just started falling is
 mg sinθ =  μN = μ mg cosθ or θ = tan-1(μ)
Answered by Expert 7th September 2018, 5:02 PM
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