Q.

In a cylindrical 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 shownin the diagram. An observer states the particle moves first undeviated and subsequently

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a

oscillates inside cylinder along a horizontal diameter passing through axis of the cylinder with time period 4RqBmg

b

oscillates inside cylinder along a horizontal diameter passing through axis of the cylinder with time period 2qRBmg

c

oscillates inside cylinder along a horizontal diameter passing through axis of the cylinder with time period mgqBR

d

It is not possible for the particle to oscillate in this given situation.

answer is D.

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Detailed Solution

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 1st collision, qvB and mg start acting in same direction along vertical and the particle is not able to move in horizontal plane.
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In a cylindrical 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 shownin the diagram. An observer states the particle moves first undeviated and subsequently