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 gt 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.

Answer

A, B, C

Explanation

From conservation of energy
`U_i+K_i=U_f+K_f` ltbr.gt `or qV_i+K_i=qV_f+K_f`
`or q(Q/(4piepsilon_0r))+1/2mv^2`
`=q(Q/(4piepsilon_0R^3))(1.5r^2-0.5R^2/4)+0`
`1/2mv^2=(11Qq)/(3piepsilon_0R)-(Qq)/(4piepsilon_0r)`
or `v=sqrt((Qq)/(2piepsilon_0mR)((r-R)/r+3/8))`