A positive charge Q is uniformly distributed throughout the volume of a dielectric sphere of radius R. A point mass having charge +q and mass m is fired toward the center of the sphere with velocity v from a point at distance r(r>R) from the center of the sphere. Find the minimum velocity v so that it can penetrate (R/2) distance of the sphere. Neglect any resistance other than electric interaction. Charge on the small mass remains constant throughout the motion.

