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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 is proportional to

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$x + y$

$x - y$

$\frac{x + y}{r}$

$\frac{x - y}{r}$

answer is D.

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Detailed Solution

$v_{0} = \frac{2}{9} \frac{r^{2} (ρ - ρ_{l}) g}{η} ρ V = x - - - (1) ρ_{l} V = y - - - (2) (ρ - ρ_{l}) V = x - y (ρ - ρ_{l}) = \frac{x - y}{\frac{4 {πr}^{3}}{3}}$

Now, $x = \frac{4}{3} {πr}^{3} ρ or ρ \propto \frac{x}{r^{3}}$

Similarly, $ρ^{'} \propto \frac{y}{r^{3}}$

$∴ v_{0} \propto \frac{x - y}{r}$

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