A bead of mass m is released from rest at A to move along the fixed smooth circular track as shown in figure. The ratio of magnitudes of centripetal force and normal reaction by the track on the bead at any point P0 described by the angle θ(≠0) would
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a
Increase with θ
b
Decrease with θ
c
Remain constant
d
First increase with θ and then decrease
answer is C.
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Detailed Solution
Conservation of energy gives 12mv2=mgRsinθ⇒mv2R=2mgsinθ=FC Now, N−mgsinθ=FC⇒N=3mgsinθ∴ FCN=23