In a cylinderical region uniform magnetic field is present as shown in the figure. The cylinder is kept on a horizontal plane and its axis is horizontal. If a charge particle of mass `m` and charge `q` is projected horizontally with velocity `v` through a hole normal to the axis of the cylinder as shown in the diagram. An observer states the particle moves first undeviated and subsequently. oscillates inside cylinder along a horizontal diameter passing through axis of the cylinder time period

Options

A. oscillates inside cylinder along a horizontal diameter passing through axis of the cylinder time period `(4RqB)/(mg)`
B. oscillates inside cylinder along a horizontal diameter passing through axis of the cylinder time period `(2qRB)/(mg)`
C. oscillates inside cylinder along a horizontal diameter passing through axis of the cylinder time period `(mg)/(qBR)`
D. It is not possible for the particle to oscillates in this given situation

Answer

D

Explanation

Consider the `2D` view of the situation. Before any collision with the walls of cylinder, the particle will move in horizontal plane if `qvB=mg`.

But after `1^(st)` collision, `qvB` and `mg` starts acting is not able to move in horizontal plane.