Electrostatic question jee

Question

A unit positive charge of mass m is projected with a velocity v inside the tunnel which has been made inside a uniformly charged non-conducting sphere. Find the minimum velocity with which a point charge should be projected from one end of the tunnel so that it can reach the opposite end of the tunnel.

physics electrostatic question NO.33

ANSWER: A

Answer 1

We consider the charge in the sphere to be positive because if it is negative then zero velocity will be needed by the particle to reach the opposite end.

Here,

Mass of the projectile = M

Radius = R

Let charge on the sphere = Q

Charge of the projectile = 1 C

The electric field inside the non-conducting charged sphere at a distance r from the center is given by