Question #42514

A large chamber is filled with an ideal gas of molecule mass $m$ and uniform number density $n$ at temperature $T$. A thin, flat plate of area $A$ and mass $M_p$ is placed inside the chamber. The chamber is then accelerated with a constant acceleration $a$ in a gravity-free space, in a direction normal to the plate. Assume the acceleration $a$ is small enough that the local gas density $n$ around the plate remains uniform. All collisions between the gas molecules and the plate are perfectly elastic. Eventually, the plate reaches a steady terminal velocity $u$ relative to the chamber ($u \ll \bar{v}$, where $\bar{v}$ is the mean speed of the gas molecules). Which of the following expressions gives the correct value of $u$? (Ignore any edge effects of the plate, and let $k$ be the Boltzmann constant).