A marble of mass x and diameter 2 r is gently released in a tall cylinder containing honey. If the marble displaces mass y(

Question

A marble of mass x and diameter 2 r 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 (A) x+y (B) x-y (C) (x+y/r) (D) (x-y/r)

Tardigrade Admin · Accepted Answer

v0=(2/9) (r2(ρ-ρ prime) g/η) Now, x=(4/3) π r3 ρ or ρ propto (x/r3) Similarly, ρ prime propto (y/r3) ∴ v0 propto (x-y/r)

Q. A marble of mass $x$ and diameter $2 r$ 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

$x + y$

$x - y$

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

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

$v_{0} = \frac{2}{9} \frac{r ^{2} ( ρ - ρ ^{'} ) g}{η}$
Now, $x = \frac{4}{3} π r^{3} ρ$ or $ρ \propto \frac{x}{r ^{3}}$
Similarly, $ρ^{'} \propto \frac{y}{r ^{3}}$
$∴ v_{0} \propto \frac{x - y}{r}$

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 is proportional to

x+y

x−y

rx+y​

rx−y​