A positive charge \( Q \) is uniformly distributed throughout \( \mathrm{P} \) the volume of a d...

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A positive charge \( Q \) is uniformly distributed throughout
\( \mathrm{P} \) the volume of a dielectric sphere of radius \( R \). A point mass having charge \( +q \) and mass \( m \) is fired towards the centre of the W sphere with velocity \( v \) from a point at distance \( x \) from the centre 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 :
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