A particle is at rest with respect to the wall of an inverted cone rotating with uniform angular velocity `omega` about its central axis. The displacement of particle along the surface up or down, the equilibrium of particle is

Options

A. stable
B. unstable
C. neutral
D. None of these

Answer

B

Explanation

Let us see the `FBD` with respect to rotating cone (non-inertial)

`N,F` and `mg` are balanced in the shown diagram. If displaced upwards, `F` will increase as `R` is increased. This will have a component up the plane. So, it will move upwards. Hence, the equilibrium is unstable.