A bullet of mass `m` and charge q if fired towards a solid uniformly charged sphere of radius R and total charge `+q`. If strikes the surface of sphere with speed `u`, find the minimum speed `u` so that it can penetrate through the sphere (Neglect all resistance forces or friction acting on bullet except electrostatic forces)

Options

A. `(q)/(sqrt(2 pi epsi_(0) m R))`
B. `(q)/(sqrt(4 pi epsi_(0) m R))`
C. `(q)/(sqrt( 8 pi epsi_(0) m R))`
D. `sqrt( 4 pi epsi_(0) m R)`

Answer

B

Explanation

Applying conservation of energy between surface and center
`K_s+ U_s =K_c+U_c,1/2 m u^2 +q. q/(4 pi e_0R)=0+q. (3q)/( 8 pi e_0R) , 1/2 m u^2=1/8. q^2/( pi e_0 R)`
`u^2 =q^2/ ((4 pi e_0 m R) implies u=q/sqrt(4 pi e_0 mR)`