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 ?
Text Solution
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(a, b, c)
u' = α u, α = constant
w.r.t plane
F leading = 2 ρ A(u' + v) 2
F trailing = 2 ρ A(u' – v) 2
F leading – F trailling = 2 ρ A(4u'v) = 8 ρ Au'v
Pressure difference = 
= 8 ρ u'v = 8 ρα uv
Net force on plate
F net = F – 8 ρ A α uv = 
After long time v will be sufficient so F = 8 ρ A α uv
After that v = constant, i.e. plate will achieve terminal velocity.
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