Motion of a ball bearing inside a smooth curved bowl, when released from a point slightly above the lower point is

Options

A. simple harmonic motion
B. non-periodic motion
C. periodic motion
D. periodic but not `SHM`

Answer

A, C

Explanation

For small angular displacement, the situation is shown in the figure. Only one restoring force creates motion in ball inside bowl.
`F =- mg sin theta`
As `theta` is small, `sin theta = theta`
So, `ma = - mg (x)/(R )`
or, `a =- ((g)/(R )) rArr a alpha - x`
So, motion of the ball is `S.H.M.` and periodic.