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Two metal spheres of densities in the ratio 3 : 2 and diameter

Question

Two metal spheres of densities in the ratio $3 : 2$ and diameter in the ratio $1 : 2$ are released from rest in two vertical liquid columns of coefficients of viscosity in the ratio $4 : 3$ . If the viscous force on them is the same then the ratio of their instantaneous velocities is :

1 : 2

3 : 2

4 : 3

8 : 3

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Samuel Discussed

Two metal spheres of densities in the ratio

3 : 2

and diameter in the ratio

1 : 2

are released from rest in two vertical liquid columns of coefficients of viscosity in the ratio

4 : 3

. If the viscous force on them is the same then the ratio of their instantaneous velocities is :

13 mins ago

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13 mins ago

Text solutionVerified

According to Stokes law, when a spherical body of radius

r

is falling in a homogeneous fluid of viscosity

η

, the viscous drag acting on body is given by

F = 6 π ηr v

Since viscous drag on both side are equal then,

6 π η_{1} r_{1} v_{1} = 6 π η_{2} r_{2} v_{2}

So,

\frac{v _{1}}{v _{2}} = \frac{η _{2}}{η _{1}} . \frac{r _{2}}{r _{1}}

= \frac{3}{4} \times \frac{2}{1} = 3 : 2

The ratio of the instantaneous velocities is

3 : 2

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Question Text	Two metal spheres of densities in the ratio $3 : 2$ and diameter in the ratio $1 : 2$ are released from rest in two vertical liquid columns of coefficients of viscosity in the ratio $4 : 3$ . If the viscous force on them is the same then the ratio of their instantaneous velocities is :
Answer Type	Text solution:1
Upvotes	151