Question

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

Answer 1

Given :

The force of repulsion between the bullet and solid sphere F=KQq/R² ----------(1)

Force acting on bullet=Fbullet=F=ma---------(2)

These two forces are equal ,

hence

ma=KQq/R²

a=KQq/mR²--------(3)

Given that bullets strikes the surface of sphere with speed u and let s be the distane it penetrates.

Then
v²-u²=2as

final velocity will be zero, so

a=-a;u²=2as

s=u²/2a

from equation (3) we get 

s=u²/2a=u2 kQq/2mR²

2R=u²mR²/2kQq

4KQq/mR=u²

u=2√KQq/mR