A flat plate is moving normal to its plane through a gas under the action of a constant force F. The gas is kept at a very low pressure. The speed of the plate v is much less than the average speed u of the gas molecules. Which of the following options is/are true?

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At a later time the external force F balance the resistance force

The plate will continue to the move with constant non-zero acceleration, at all times

The resistive force experienced by the plate is proportional to v

The pressure difference between the leading and trailing faces of the plate is proportional to uv

answer is A.

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Detailed Solution

S → area of plateFor left side particles,v−(−u)=v1−v⇒v1=u+2v Change in momentum =ΔP1=mvf−vi=mv1−(−u)=m(2u+2v) Force applied by left side particles on plate =F1=ΔP1Δt=ρA(u+v)(2u+2v) For right side particles, v−u=v−−v2⇒v2=u−2v Change in momentum =ΔP2=mvf−vi=m−v2−u=−m(2u−2v) Force applied by right side particles on plate =F2=ΔP2Δt=ρA(u−v)(2u−2v) Resistive force on plate =ΔF=F1−F2=8ρ Auv Pressure difference =ΔFA=8ρuV Net force, F−△F=ma⇒F−8ρAuV=maAfter long time, resistance can balance external force.

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