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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

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a

directly proportional to R  but inversely proportional to v

b

directly proportional to radius R and velocity v

c

inversely proportional to both radius R andvelocity v

d

inversely proportional to radius r but directly proportional to velocity v

answer is B.

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Detailed Solution

The retarding force on a ball falling into a viscous fluid is given byF=6πηRv  where R= radius of the ball, v= velocity of ball ,  and η= coefficient of viscosity   Therefore, F∝R and F∝V
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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