Two steel balls, each of mass $m$, are welded to a light rod of length $L$ and negligible mass and are initially at rest on a smooth horizontal surface. A horizontal force of magnitude $F$ is suddenly applied to the rod as shown. Determine (a) the instantaneous acceleration $\bar{a}$ of the mass center $G$ and $(b)$ the corresponding rate $\ddot{\theta}$ at which the angular velocity of the assembly about $G$ is changing with time.