Q. A particle of mass is released from point on smooth fixed circular track as shown. If the particle is released from rest at then variation of normal reaction with angular displacement from initial position is -

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Solution:

When the block reaches a point where the angular displacement from the initial position is as shown.

The normal reaction force on the mass is
.
Here, is the centrifugal force on the mass.
By conservation of mechanical energy,


The Normal reaction,

.
Therefore, the normal reaction varies sinusoidally with as