JEE Advanced2017PhysicsCenter of Mass, Momentum and CollisionActual
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 I much less than the average speed u of the gas molecules. Which of the following options is true?
Options
- AAt a later time the external force F balances the resistive force
- BThe resistive force experienced by the plate is proportional to v
- CThe plate will continue to move with constant non zero acceleration at all times
- DThe pressure difference between the leading and trailing faces of the plate is proportional to u v
Correct answer
A. At a later time the external force F balances the resistive force
Step-by-step solution
v 1 = u + 2 v v 2 = u - 2 v Δ v 1 = 2 u + 2 v Δ v 2 = 2 u - 2 v F 1 = d p 1 d t = ρ A u + v 2 u + 2 v F 2 = d p 2 d t = ρ A u - v 2 u - 2 v = 2 ρ A u + v 2 = 2 ρ A u - v 2 Δ F = F 1 - F 2 ( Δ F net force due to the air molecules on the plate) = 2 ρ A 4 u v = 8 ρ A u v P = Δ F A = 8 ρ u v F n e t = F - Δ F = m a (m is mass of the plate) F - 8 ρ A u v = m a