A solid sphere has linear velocity ${\text{v}}_0=4\; m/s$ and angular velocity ${\omega }_0=\text{9 rad/s}$ as shown. Ground on which it is moving, is smooth. It collides elastically with a rough wall of coefficient of friction $\mu$. Radius of the sphere is 1 m and mass is 2 kg.



If the sphere after colliding with the wall rolls without slipping in opposite direction, then coefficient of friction $\mu$  is