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Question:

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?

At a later time the external force F balances the resistive force

The resistive force experienced by the plate is proportional to v

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

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

Solution:

v1=u+2vΔV1=(2u+2v)F1=dp1dt=ρA(u+v)×(2u+2v)=2ρA(u+v)2v2=(u−v)Δv2=2u−2vF2=dp2dt=ρA(u−v)×(2u−2v)=2ρA(u−v)2AsF1andF2are acting in opposite direction soFnet=F1−F2=2ρA(4uv)=8ρAvuP=ΔFA=8ρuvFnet=(F−ΔF)=mam is the mass of the plate.F−(8ρAuv)=ma