Class 11

Physics

Mechanics

Mechanical Properties of Fluids

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?

- The resistive force experienced by the plate is proportional to $v$
- At a later time the external force $F$ balances the resistive force
- The plate will continue to move with constant non-zero acceleration, at all times
- The pressure difference between the leading and trailing faces of the plate is proportional to $uv$

$v_{1}=u+2v$

$ΔV_{1}=(2u+2v)$

$F_{1}=dtdp_{1} =ρA(u+v)×(2u+2v)=2ρA(u+v)_{2}$

$v_{2}=(u−2v)$

$Δv_{2}=2u−2v$

$F_{2}=dtdp_{2} =ρA(u−v)×(2u−2v)=2ρA(u−v)_{2}$

As $F_{1}$ and $F_{2}$ are acting in opposite direction so

$F_{net}=F_{1}−F−2=2ρA(4uv)=8ρAvu$

$P=AΔF =8ρuv$

$F_{net}=(F−ΔF)=ma$ m is the mass of the plate.

$F−(8ρAuv)=ma$