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A flat plate moves perpendicular to its plane through a gas at low pressure under a constant force F. The plate speed v is much less than the average molecular speed u. Which of the following statements is/are true? (A) The resistive force on the plate is proportional to v. (B) The pressure difference between the leading and trailing faces is proportional to u*v. (C) The plate continues to accelerate at constant non-zero acceleration at all times. (D) At a later time, the external force F balances the resistive force.

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

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

Solution

Resistive force is proportional to v (A is true). Pressure difference is proportional to uv (B is true). The plate does NOT have constant non-zero acceleration at all times — as v increases, so does resistive force, until it equals F and acceleration becomes zero (C is false). At some point F equals resistive force (D is true). So A, B, D are true. The question asks which option is true — if single answer, the most fundamental is A.

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