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A collar B of mass 2 kg is constrained to move along a horizontal smooth and fixed circular track of radius 5 m. The spring lying in the plane of the circular track and having spring constant 200 N m^-1 is undeformed when the collar is at A. If the collar starts from rest at B, the normal reaction exerted by the track on the collar when it passes through A is

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2880 N

1440 N

360 N

720 N

answer is C.

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Detailed Solution

Initial extension will be equal to 6 m.
Initial energy $= \frac{1}{2} (200) (6)^{2} = 3600 J$

Reaching A, we get $\frac{1}{2} {mv}^{2} = 3600 J$

From FBD at A, we get $N = \frac{{mv}^{2}}{R} = \frac{7200}{5} = 1440 N$

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