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Spherical balls of radius 'R' are fallin...

Spherical balls of radius 'R' are falling in a viscous fluid of viscosity `'eta'` with a velocity 'v'. The retarding viscous force acting on the spherical ball is

A

directly proportional to `R` but inversely propotional to `v`

B

directly propotional to both radius `R` and velocity `v`

C

inversely propotional to both radius `R` and velocity `v`

D

inversely propotional to `R` but directly propotional to `v`

Text Solution

Verified by Experts

The correct Answer is:
B
Retarding force acting on a ball falling into a viscous fluid
`F = 6pietaRv`
where `R =` radius of ball,
`v =` velocity of ball.
and `eta = ` coefficient of viscosity
`:. F prop R` and `F prop v`
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Knowledge Check

  • When a sphere falling in a viscous fluid attains a terminal velocity, then

    A
    the net force acting on the sphere is zero
    B
    the drag force balances the buoyant force
    C
    the drag force balances the weight of the sphere
    D
    the buoyant force balances the weight and drag force

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    R
    B
    `(1)/(R)`
    C
    `R^(2)`
    D
    `(1)/(R^(2))`

  • A drop of water of radius r is falling rhough the air of coefficient of viscosity eta with a constant velocity of v the resultant force on the drop is

    A
    `(1)/(6pietarv)`
    B
    `6pietarv`
    C
    `sqrt(6pietarv)`
    D
    zero

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