A marble of mass $x$ and diameter $2 r$ is gently released in tall cylinder containing honey. If the marble displace mass $y (< x)$ of the liquid, then the terminal velocity is proportional to

x + y

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x - y

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\frac{x + y}{r}

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\frac{x - y}{r}

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Solution

The correct option is D $\frac{x - y}{r}$
If $v$ is the terminal velocity, then we have
$x g - y g = 6 π μ r v$
Hence $v = \frac{(x - y) g}{6 π μ r}$

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A marble of mass x and diameter 2r is gently released in tall cylinder containing honey. If the marble displace mass y(<x) of the liquid, then the terminal velocity is proportional to

The correct option is D x−yrIf v is the terminal velocity, then we havexg−yg=6πμrvHence v=(x−y)g6πμr

A marble of mass $x$ and diameter $2 r$ is gently released in tall cylinder containing honey. If the marble displace mass $y (< x)$ of the liquid, then the terminal velocity is proportional to

The correct option is D $\frac{x - y}{r}$
If $v$ is the terminal velocity, then we have
$x g - y g = 6 π μ r v$
Hence $v = \frac{(x - y) g}{6 π μ r}$