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

Explanation

Initially ,
Length of spring = 13 m
undeformed length = 7 m
Initial extention `(x_("in")) = 13 – 7 = 6`

final extension `(x_(f)) = 0`
Applying work energy theorem for motion from B to A
`(1)/(2)k(x_("in")^(2)-x_(f)^(2))=(1)/(2)mv^(2)`
`mv^(2)=200(y^(2)-0^(2))=200xx49`
`mv^(2)=9800`
At point A, along radial direction, `F_("net")=N=m(v^(2))/(R)`

`therefore N=(mv^(2))/(R)=(9800)/(5)`
`=(200)/(5)[0-(6)^(2)]`
= 1960 Newton