`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 `Fgt2 mg`
B. At `B`, the normal reaction of the track is `F-2 mg`
C. At `D`, the normal reaction of the track is `F+2 mg`
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=1/2mv^(2)=mgr,(mv^(2))/r=2mg`
`F-N=(mv^(2))/r=2mg,F=N+2mg`
as `N ge 0 F ge 2mg,` at `B F-N=2mg`
at `D N-F=2mg`