- 1. 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 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?

Options- A. The pressure difference between the leading and trailing faces of the plate is proportional to uv
- B. 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
- D. At a later time the external force F balances the resistive force Discuss

Correct Answer: A, B, D

n = number of molecules per unit volume

u = average speed of gas molecules

When the plate is moving with speed v, the relative speed of molecules w.r.t. leading force = v + u

Coming head-on, momentum transformed to plate per collision = 2m(u + v)

Number of collision in time: Δt = ((v + v_{0})nΔtA)/2

where A = Surface area

So, momentum transferred in time Δt = m(u + v)^{2}nAΔt from front surface

Similarly momentum transferred in time = m(u – v)^{2}nAΔt from back surface

Net force = mnA[(v + u)^{2} – (u – v)^{2}]

= mnA[4vu]

F ∝ v

P_{leading}– P_{trailing }= mn[u + v]^{2} – mn[u – v]^{2}

= mn[4uv]

= 4mnuv

ΔP ∝ uv

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