A non-uniform ball of radius R and radius of gyration about geometric centre `=R//2` is kept on a frictionless surface. The geometric centre coincides with the centre of mass. The ball is struck horizontally with a sharp impulse `=J` the point of application of the impulse is at a height `h` above the surface. then.

Options

A. The ball will slip on surface for all cases
B. The ball will roll purely if h=5R/4
C. The ball will roll purely if h=3R/2
D. The ball will roll purelly if `h=5R/3`

Answer

2

Explanation

`J=mv.....(1)`
`Jx=((mR^(2))/4)omega.......(2)`
`v=omegaR`
`x=R/4, h=(5R)/4`
If `h=Rx =0`
`omega=0` (from eq-2)