A solid ball of mass $$M$$ and radius $$R$$ is lying on a horizontal table. The ball experiences a short horizontal impulse which imparts a momentum $$p$$ to the ball. The height of point of impact above the center line is $$h=\alpha R$$, where $$0\le\alpha\le1$$. Choose the correct option or options.

A

Translational energy of the ball is $$\frac{p^2}{2M}$$

B

Energy of pure rotational motion of the ball is $$\frac{5p^2\alpha^2}{4M}$$

C

For $$\alpha=\frac25$$, the ball rolls without sliding

D

For $$\alpha=0$$, pure rotational motion will be observed