A uniform solid sphere of mass m and radius R having initial angular velocity ${\omega }_0=\frac{3V_0}{2R}$ and moving with initial velocity $(v_0\widehat{i}-v_0\widehat{j})$ collides with a rough horizontal surface $(\mu =0.4)$ with a coefficient of restitution $e=0.5$ as shown in the figure. The angular velocity of the sphere just after collision becomes $\omega$ rad/s and the impulse due to friction on the sphere is $Jkg-m/s. (Takem=4.8kg,R=32cmand{v}_0=3.5m/s)$