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Two spheres of the same material, but of radii R and 3R are al

Question

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

1 : 3

1 : 6

1 : 9

1 : 1

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Two spheres of the same material, but of radii

R

and

3 R

are allowed to fall vertically downwards through a liquid of density

ρ

. The ratio of their terminal velocities is:

15 mins ago

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15 mins ago

Text solutionVerified

Terminal velocity of the sphere

v = \frac{2 g r ^{2} ( σ - ρ )}{9 η}

where

η

is the viscosity of the liquid,

σ

is the density of material of sphere,

ρ

is the density of liquid and

r

is the radius of the sphere.

⟹

v \propto r^{2}

Given :

r_{1} = R

and

r_{2} = 3 R

Ratio of terminal velocities

v_{1} : v_{2} = r_{1}^{2} : r_{2}^{2}

v_{1} : v_{2} = R^{2} : (3 R)^{2}

⟹

v_{1} : v_{2} = 1 : 9

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Question Text	Two spheres of the same material, but of radii $R$ and $3 R$ are allowed to fall vertically downwards through a liquid of density $ρ$ . The ratio of their terminal velocities is:
Answer Type	Text solution:1
Upvotes	150