Spherical balls of radius ‘R’ are falling in a viscous fluid of viscosity ‘?’ with a velocity ‘v’. The retarding viscous force acting on the spherical ball is:

Question

Spherical balls of radius $‘ R ’$ are falling in a viscous fluid of viscosity $‘ η ’$ with a velocity $‘ v ’$ . The retarding viscous force acting on the spherical ball is:

Smart Achievers · Accepted Answer

(2)

From Stoke's law, force of viscosity acting on a spherical body is $F = 6 π η r v$

Hence, $F$ is directly proportional to radius and velocity.

Solution

Q.
Spherical balls of radius $‘ R ’$ are falling in a viscous fluid of viscosity $‘ η ’$ with a velocity $‘ v ’$ . The retarding viscous force acting on the spherical ball is:

1 inversely proportional to both radius $‘ R ’$ and velocity $‘ v ’$

2 directly proportional to both radius $‘ R ’$ and velocity $‘ v ’$

3 directly proportional to $‘ R ’$ but inversely proportional to $‘ v ’$

4 inversely proportional to $‘ R ’$ but directly proportional to velocity $‘ v ’$

Ans.
(2)

From Stoke's law, force of viscosity acting on a spherical body is $F = 6 π η r v$

Hence, $F$ is directly proportional to radius and velocity.

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Solution

Q. Spherical balls of radius ‘R’ are falling in a viscous fluid of viscosity ‘η’ with a velocity ‘v’. The retarding viscous force acting on the spherical ball is:

1 inversely proportional to both radius ‘R’ and velocity ‘v’

2 directly proportional to both radius ‘R’ and velocity ‘v’

3 directly proportional to ‘R’ but inversely proportional to ‘v’

4 inversely proportional to ‘R’ but directly proportional to velocity ‘v’

Ans. (2) From Stoke's law, force of viscosity acting on a spherical body is F=6πηrv Hence, F is directly proportional to radius and velocity.