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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

Arun
24742 Points
							dF = dP/dTwhere F = mg, and P = mvMg = d(MV)/ dT = M dV/ d t + V dM/ d tsince dM/ d t = kMVkV2 + dV/d t = gThen we can see, as the drop falls, it’s velocity increases due to gravity. However, thereis a limit for this velocity because as the drop speeds up, its acceleration decreases rapidlyand will become negligible as the time goes to infinity. So the speed of the drop willeventually become constant.To compute the terminal constant speed, we could set dV/d t = 0 then we have k Vt2 = gVt = $\sqrt$(g/k)

3 years ago
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### Course Features

• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions