JEE Advanced · 2017 · 21 May 2017 · Paper 1 · Heat & Thermodynamics

At low pressure, the gas molecules collide with the plate independently. The pressure difference arises from the momentum transfer of molecules hitting the leading face (with relative speed $u+v$) versus those hitting the trailing face (with relative speed $u-v$). Since $v\ll u$, the net momentum transfer per unit time is proportional to $uv$, making option (A) correct. This momentum transfer creates a resistive force proportional to $v$, confirming option (B). Initially, the plate accelerates under force $F$. As speed increases, the resistive force (proportional to $v$) grows until it balances $F$, after which the plate moves with constant velocity, making option (D) correct and option (C) incorrect.