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 is `h=(5R)/4`
C. the ball will roll purely if `h=(3R)/2`
D. there will be no rotation if `h=R`

Answer

B, D