Discussion Forum

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 very low pressure. The speed of the plane v is much less than the average speed u of the gas molecules. Which of the following options is/are true?

Answer:

Explanation:

Just before the collision                            Just after the collision

                   $v_{1}=u+2v$

              $\triangle v_{1}=(2u+2v)$

$F_{1}=\frac{\text{d} \rho _{1}}{\text{d}t}$

   =  $\rho A(u+v)(2u+2v)$

   =  $2 \rho A(u+v)^{2}$

  $v_{2}=(u-2v)$

 $\triangle v_{2}=(2u-2v)$

$F_{2}=\frac{\text{d} \rho _{2}}{\text{d}t}$

= $\rho A(u-v)(2u-2v)$

          $=2 \rho A(u-v)^{2}$

[$\triangle F$   is the net force due to the air molecules on the plate]

      $\triangle F=2 \rho A(4uv)=8 \rho Auv$

    $P= \frac{\triangle F}{A}=8 \rho (uv)$

$F_{net}= (F-\triangle F) =ma$

                         [m is mass of the plate]

   $F -(8 \rho Au)v=ma$