The figure below shows a block of mass M connected to an ideal string which passes through a thin fixed smooth pipe. On the other end, a particle of mass rn is connected which revolves in a vertical circle of radius r. If the coefficient of friction between M and the surface is 
, then for what minimum value of M, the block of mass m can undergo complete vertical circular motion?
Text Solution
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M min = 9m
For the particle to undergo complete vertical circular motion, its speed at the lowest point should be at least 
. Also, the tension in the string is maximum when the particle is at the lowest point. The tension at the lowest position of the particle is
The friction force acting on the block should be able to balance the maximum tension.
f = T = 6mg
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