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Question

A marble of mass x and diameter 2r is gently released in a tall cylinder containing honey. If the marble displaces mass y(<x) of the liquid, then the terminal velocity is proportional to
  1. x+y
  2. xy
  3. x+yr 
  4. xyr 


Solution

The correct option is D xyr 
We know that,
v0=2 r2(ρρ,)g9 η
Now,
x=43πr3ρ or ρxr3

Similarly, ρ,yr3
So, if we substitute both values into equation of v0 we get,
v0xyr
 

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