Properties of Matter 4 Question 11

13. A flat plane 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?

(2017 Adv.)

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

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

(c) The resistive force experienced by the plate is proportioal to v

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

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Answer:

Correct Answer: 13. 6

Solution:

  1. From mass conservation,

ρ43πR3=ρK43πr3R=K1/3rΔΔU=TΔA=T(K4πr24πR2)=T(K4πR2K2/34πR2)ΔU=4πR2T[K1/31]

Putting the values, we get

103=1014π×4π×104[K1/31]

100=K1/31K1/3100=102 Given that K=10α10α/3=102α3=2α=6



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