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Grade: 12th pass

                        

a raindrop of initial mass M0 starts falling from restunder the influence of gravity.the drop gains mass from the cloud at a rate proportional to the protect of its instantaneous mass and vrlocity,show that the drop eventually attains a terminal speed,determining it.

3 years ago

Answers : (1)

Arun
24742 Points
							
dF = dP/dT
where F = mg, and P = mv
Mg = d(MV)/ dT = M dV/ d t + V dM/ d t
since 
dM/ d t = kMV
kV2 + dV/d t = g
Then we can see, as the drop falls, it’s velocity increases due to gravity. However, there
is a limit for this velocity because as the drop speeds up, its acceleration decreases rapidly
and will become negligible as the time goes to infinity. So the speed of the drop will
eventually become constant.
To compute the terminal constant speed, we could set dV/d t = 0
 
then we have 
k Vt2 = g
Vt = \sqrt(g/k)
3 years ago
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