Physics problems
- 1. 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 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?
Options- A. The pressure difference between the leading and trailing faces of the plate is proportional to uv
- B. resistive force experienced by the plate is proportional to v
- C. The plate will continue to move with constant non-zero acceleration, at all times
- D. At a later time the external force F balances the resistive force Discuss
Correct Answer: A, B, D
Explanation:
n = number of molecules per unit volume
u = average speed of gas molecules
When the plate is moving with speed v, the relative speed of molecules w.r.t. leading force = v + u
Coming head-on, momentum transformed to plate per collision = 2m(u + v)
Number of collision in time: Δt = ((v + v0)nΔtA)/2
where A = Surface area
So, momentum transferred in time Δt = m(u + v)2nAΔt from front surface
Similarly momentum transferred in time = m(u – v)2nAΔt from back surface
Net force = mnA[(v + u)2 – (u – v)2]
= mnA[4vu]
F ∝ v
Pleading– Ptrailing = mn[u + v]2 – mn[u – v]2
= mn[4uv]
= 4mnuv
ΔP ∝ uv
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