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A flat plate is pushed through a very low-pressure gas by a constant force F, moving perpendicular to its plane. The plate's speed v is much smaller than the average molecular speed u of the gas. Which of the following statements are correct? (A) The resistive force on the plate is proportional to v. (B) The pressure difference between the leading and trailing faces is proportional to uv. (C) The plate continues to accelerate at a constant non-zero rate at all times. (D) Eventually the external force F is balanced by the resistive force.

1. (A) The resistive force experienced by the plate is proportional to v
2. (B) The pressure difference between the leading and trailing faces of the plate is proportional to uv
3. (C) The plate will continue to move with constant non-zero acceleration, at all times
4. (D) At a later time the external force F balances the resistive force.

Correct answer: (A) The resistive force experienced by the plate is proportional to v

Solution

The momentum flux to each face gives pressure proportional to the square of relative molecular speed. The pressure difference scales as 4uv (B correct), and since u is a constant of the gas, the resistive force also scales with v (A correct). As v increases under constant F, the net force decreases and acceleration is not constant (C false). Terminal velocity is reached when F equals resistive force (D correct).

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