Question

A bullet of mass m and charge `q` is fired towards a solid unifromly charged sphere of redius `R ` and total cbharge ` + q`. If it strikes the surface of sphere with speed `u`, find the minimum speeed `u` so that it can penetrate through the sphere , (Neglect all resistance forces or friction acting on bullet except electrositatic forces )
.
A. `(q)/(sqrt(2 pi varepsilon_(0)mR)`
B. `(q)/(sqrt(4 pi varepsilon_(0)mR)`
C. `(q)/(sqrt(8 pi varepsilon_(0)mR)`
D. `(sq)rt3q/(sqrt(4 pi varepsilon_(0)mR)`

Answer 1

Correct Answer - B
` v_s` = Potential at surfce `= 1/ (4 pi in_0 ) q/R`
` V_("in") = (KQ(3R^2-r^2))/(2R^3)`
`V_0 = 3/2 1/(4 pi in_0 ) q/R`
To pentrate it must reach cenyre of sphere.
From energy conservation
`1/2 mu^2 _ 1/ ( 4 pi in_0 ) (q.q)/R =0 + 3/2 . 1/( 4 pi in _0 ), (qq)/R`
` 1/2 mu^2 = 1/2 1/(4 pi in_0 ) q^2/R , E= (mg)/(2q)`
`u^2 = q^2 /(4 pi in_0 mR)`
`u = q/sqrt (4 pi in_0 mR)`.