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A flat plate is moving normal to its pla...

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 ?

A

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

B

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

C

At a later time external force F balances the resistive force

D

At a later time external force F balances the resistive force

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Molecules hitting the forward and rear surfaces will bounce back with speeds given above. Let mass of one molecule be `m_0`. Then,
`Delta P_0` (forward) `= 2m_0 (u +v)`
`Delta P_0 `(Rear) ` = 2m_0 (u -= v)`
Let the rates of collision with front and rear surfaces be `R_1` and `R_2` respectively
So, `R_1 alpha (u + v)`
`R_2 alpha ( u - v)`
Force = `Delta P. R.`
So, `F_1 = R_1 2m_0 (u + v),F_2 = R_2 .2m_0 (u - v)`
So, `F_1 - F_2 alpha 2m_0 (u +v)^@ - 2m_0 (u-v)^2`
`alpha 2m_0 [4uv]`
`alpha uv` So, (A) is correct
Clearly, the net force due to gas is proportion to i.e. it is variable hence acceleration of plate is variable.
Finally the plate will start moving with terminal velocity.
Hence (C) is correct.
Resistive force `= Delta P.A prop V" "rArr" Hence (D) is correct "`
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