Figure shows a smooth track, a part of which is a circle of radius R. A block of mass m is pushed against a spring constant 
fixed at the left end and is then released. Find the initial compression of the spring so that the block presses the track with a force mg when it reaches the point P [see. Fig], where the radius of the track is horizontal
Text Solution
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For the given condition, centrifugal force at P should be equal to mg i.e. 
From this we can easily calculate the required velocity at the lowest point of circular track.
(by using formula: 
)
It means the block should possess kinetic energy 
And by the law of conservation of energy
⇒ ⇒ 
.
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