A flat plate is moving normal to its plane through a gas under the action of a constant forceF. The gas is kept at a very low pressure. The speed of the plate v is much less than theaverage speed u of the gas molecules. Which of the following options is/are true?[A] The pressure difference between the leading and trailing faces of the plate isproportional to uv[B] The resistive force experienced by the plate is proportional to v[C] The plate will continue to move with constant non-zero acceleration, at all times[D] At a later time the external force F balances the resistive force

The question is asking about the behavior of a flat plate moving through a gas under certain conditions. Let's analyze each option:

[A] The pressure difference between the leading and trailing faces of the plate is proportional to uv. This is true. The pressure difference is caused by the momentum transfer of the gas molecules hitting the plate, which is proportional to their average speed (u) and the speed of the plate (v).

[B] The resistive force experienced by the plate is proportional to v. This is also true. The resistive force (also known as drag) is proportional to the square of the velocity of the object moving through the fluid. In this case, since the speed of the plate (v) is much less than the average speed of the gas molecules (u), the resistive force can be approximated as being proportional to v.

[C] The plate will continue to move with constant non-zero acceleration, at all times. This is not necessarily true. The acceleration of the plate will depend on the balance between the applied force (F) and the resistive force. If the resistive force equals the applied force, the plate will move with constant velocity, not acceleration.

[D] At a later time the external force F balances the resistive force. This is true. As the plate speeds up, the resistive force increases until it balances the applied force (F). At this point, the plate will move with constant velocity.

So, the correct options are A, B, and D.