`ABCDE` is a smooth iron track in the vertical plane. The sections `ABC` and `CDE` are quarter circles. Points `B` and `D` are very close to `C.M` is a small magnet of mass `m`. The force of attraction between `M` and the track is `F`, which is constant and always normal to the track. `M` starts from rest at `A`, then:

Options

A. If M is not to leave the track at C ,then F `gt 2 mg`
B. At B , the normal reaction of the track is F - 2mg
C. At D , the normal reaction of the track is F + 2mg
D. The normal reaction of the track is equal to F at some point between A and M

Answer

B, C, D

Explanation

At C = `(1)/(2) mv^(2) = mgr , (mv^(2))/(r) = 2mg`
`F - N = (mv^(2))/(r) = 2 mg `
`F = N + 2mg `
as `N ge 0 " " F ge 2 mg , at B F -N = 2mg`
at D `N -F = 2mg`