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(C) When a plate moves with speed $v$ in a gas where molecules have average speed $u$ $(v \ll u)$,the number of collisions per unit time on the front

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$A, B, D$

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(C) When a plate moves with speed $v$ in a gas where molecules have average speed $u$ $(v \ll u)$,the number of collisions per unit time on the front face is proportional to $(u + v)$ and on the back face is proportional to $(u - v)$.Each collision imparts a momentum change proportional to the relative velocity. The net resistive force $F_{res}$ is proportional to the difference in momentum transfer rates,which leads to $F_{res} \propto (u+v)^2 - (u-v)^2 = 4uv$. Since $v \ll u$,this simplifies to $F_{res} \propto uv$. Thus,the resistive force is proportional to $v$.Since $F_{res} \propto v$,the equation of motion is $m(dv/dt) = F - kv$. As $v$ increases,$F_{res}$ increases until $F_{res} = F$,at which point the acceleration becomes zero and the plate reaches a terminal velocity.Therefore,options $A$,$B$,and $D$ are correct.

$A$ 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?

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