Q38 / 54 · JEE Advanced 2017 (Paper 1) · Physics

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 I much less than the average speed u of the gas molecules. Which of the following options is true?

  • Correct answer
    A
    At a later time the external force F balances the resistive force
  • Correct answer
    B
    The resistive force experienced by the plate is proportional to v
  • C
    The plate will continue to move with constant non zero acceleration at all times
  • Correct answer
    D
    The pressure difference between the leading and trailing faces of the plate is proportional to uv

Solution

Figure

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

Figure

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

 

Hence, the correct answer is options: 'A', 'B', 'D'.

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