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A bullet of mass m and charge q is fired...

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

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)`

Text Solution

Verified by Experts

The correct Answer is:
B
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)`
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