What minimum velocity should be given to a particle of mass m, tied to a massless string, in the lowermost point so that it passee through the center after loosing vertical circular motion between points B and C ?
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Let the length of the string be
The kinetic energy of the particle at the lowermost point,
And potential energy is zero there, as we take it as base position.
Let be the kinetic energy of the particle at the point where the particle starts to fall towards the center.
And the potential energy of the particle at that point,
We know the total mechanical energy of the particle undergoing vertical circular motion is conserved.
Therefore,
In general the kinetic energy should be non - negative.
Hence the minimum velocity at the lowermost point will be,
With this velocity at the lowermost point, the particle gets stopped after traversing an angular displacement and then it moves towards the center as the tension in the string,