A collar B of mass `2kg` is constrained to move along a horizontal smooth and fixed circular track of radius `5m`. The spring lying in the plane of the circular track and having spring constant `200Nm^-1` is underformed 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

Options

A. (a) `360N`
B. (b) `720N`
C. (c) `1440N`
D. (d) `2880N`

Answer

C

Explanation

Initial extension will be equal to `6m`.
Initial energy `=1/2(200)(6)^2=3600J`
Reaching A, we get `1/2mv^2=3600J`
`mv^2=7200J`
From FBD at A, we get `N=(mv^2)/(R)=7200/5=1440N`