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Q.

Positive charge Q is uniformly distributed throughout the volume of a sphere of radius R. A point mass having charge +q and mass m is fired towards the centre of the sphere with velocity if from a point A at distance r(r>R) 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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a

None of above

b

  v=Q5πε0Rr+Rr-53

c

  v=Qq2πε0mRr-Rr+38

d

Zero

answer is B.

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Detailed Solution

From conservation of energy,

Ui+Ki=Uf+Kf or qVi+Ki=qVf+Kf

or qQ4πε0r+12mv2

=qQ4πε0R31.5R2-0.5R24+0

or   12mv2=11Qq32πε0R-Qq4πε0r

or   v=Qq2πε0mRr-Rr+38

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