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 with slip on surface for al cases
B. the ball will roll purely if `h=5R//4`
C. the ball will roll purely if `h=3R//2`
D. there will be no rotation if `h=R`

Explanation

`I=mK^(2)("where ", K=(R)/(2)=` radius of gyration)
`=m((R)/(2))^(2)=(1)/(4)mR^(2)`
Ball will roll purely if
`v=Romega`
`therefore((J)/(m))=R[(J(h-R))/((1//4)mR^(2))]`
Solving this equation we get
`h=(5R)/(4)`
Further, if ball is struck at centre of mass, there will be not rotation only translation.