Consider a sphere of mass $\text{'}m\text{'}$radius $\text{'}R\text{'}$ doing pure rolling motion on a rough surface having velocity ${\overrightarrow{V}}_0$ as shown in the Figure. It makes an elastic impact with the smooth wall and moves back and starts pure rolling after some time again.

 

Final velocity of ball will be $\frac{3}{7}{\overrightarrow{V}}_0$

Moment of impulse provided by the wall during impact about $O$ equals $2m{v}_{0}R$ in magnitude.

Change in angular momentum about $\text{'}O\text{'}$ in the entire motion equals $2m{v}_{0}R$ in magnitude.

Final velocity of ball will be $-\frac{3}{7}{\overrightarrow{V}}_0$