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Standard XII

Physics

Terminal Velocity

Two spheres o...

Question

Two spheres of the same material, but radii $R$ and $3 R$ are allowed to fall vertically downwards through a liquid of uniform density. The ratio of their terminal velocities is:

1 : 3

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1 : 6

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1 : 9

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1 : 1

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Solution

The correct option is C $1 : 9$
The terminal velocity $v = \frac{2 r^{2} (ρ - σ) g}{9 η}$
As, all other parameters are constant, therefore
$v \propto r^{2}$
$\Rightarrow \frac{V_{R}}{V_{3 R}} = \frac{{(R)}^{2}}{{(3 R)}^{2}} = \frac{1}{9}$

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Two spheres of the same material, but radii R and 3R are allowed to fall vertically downwards through a liquid of uniform density. The ratio of their terminal velocities is:

The correct option is C 1:9The terminal velocity v=2r2(ρ−σ)g9ηAs, all other parameters are constant, thereforev∝r2⇒VRV3R=(R)2(3R)2=19

Two spheres of the same material, but radii $R$ and $3 R$ are allowed to fall vertically downwards through a liquid of uniform density. The ratio of their terminal velocities is:

The correct option is C $1 : 9$
The terminal velocity $v = \frac{2 r^{2} (ρ - σ) g}{9 η}$
As, all other parameters are constant, therefore
$v \propto r^{2}$
$\Rightarrow \frac{V_{R}}{V_{3 R}} = \frac{{(R)}^{2}}{{(3 R)}^{2}} = \frac{1}{9}$