A flat plate is moving normal to its plane through a gas under the action of a constant force F. The gas is…

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

Solution

v1=u+2v

v2=u-2v

Δv1=2u+2v

Δv2=2u-2v

F1=dp1dt=ρAu+v 2u+2v

F2=dp2dt=ρAu-v 2u-2v

=2ρA u+v2

=2ρA u-v2

ΔF=F1-F2       (ΔFnet force due to the air molecules on the plate)

=2ρA 4uv=8ρAuv

P=ΔFA=8ρuv

Fnet=F-ΔF=ma    (m is mass of the plate)

F-8ρAuv=ma

 

Asked in: JEE Advanced 2017 (Paper 1)

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