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Q.

A container filled with viscous liquid is moving vertically downwards with constant speed 3v0. At the instant shown, a sphere of radius r is moving vertically downwards (in liquid) has speed v0. The coefficient of viscosity is η. There is no relative motion between the liquid and the container. Then at the shown instant, the magnitude of viscous force acting on sphere is

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a

6πηrv0

b

12πηrv0

c

18πηrv0

d

24πηrv0

answer is B.

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Detailed Solution

Relative to liquid, the velocity of sphere is 2v0 upwards.∴Viscous force on sphere = 6πηr2v0 downward                                        = 12πηrv0 downward
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A container filled with viscous liquid is moving vertically downwards with constant speed 3v0. At the instant shown, a sphere of radius r is moving vertically downwards (in liquid) has speed v0. The coefficient of viscosity is η. There is no relative motion between the liquid and the container. Then at the shown instant, the magnitude of viscous force acting on sphere is