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Q.

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 isproportional to

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a

x+y

b

x-y

c

x+yr

d

x-yr

answer is D.

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Detailed Solution

v0=29r2ρ−ρ'gη Now, x=43πr3ρ or ρ∝xr3 Similarly, ρ'∝yr3∴ v0∝x−yrII method  xg-yg=6πηrvT ⇒vT=x-yg6πηr
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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 isproportional to