Momentum and CollisionHard

Question

A non-conducting cylindrical shell of radius R is placed in uniform magnetic field. The axis of the cylinder is parallel to the direction of magnetic field. A hole is drilled in cylinder and a particle having charge q and mass m is projected with velocity v0 perpendicular to magnetic field and directed towards the axis of cylinder as shown in diagram. The particle collides elastically with inner wall of the cylinder and rebounds.
         

Options

A.The minimum no. of collisions after which it will emerge is two
B.The maximum speed v0 for which it can come out is v0 = √3
C.The minimum time in which it can come out will be
D.If the particle is projected with a velocity {where v0 = √3} it will come out after five collisions.

Solution

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