Classic Rotational Motion Problem

Classical Mechanics Level 4

A Solid sphere is rolling purely on a rough horizontal surface ( Coefficient of kinetic friction = μ) with speed of centre = V. It collides inelastically with a smooth vertical wall at a certain moment, the coefficient of restitution being \(\frac{1}{2}\). The sphere will begin pure rolling after a particular time which can be expressed in form of \(\frac{aV}{bμg}\) where a and b are co-prime.