(B) According to Stoke's Law,the viscous drag force $F$ acting on a spherical object of radius $r$ moving with a velocity $v$ through a fluid of visco

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Directly proportional to both radius $r$ and velocity $v$

(B) According to Stoke's Law,the viscous drag force $F$ acting on a spherical object of radius $r$ moving with a velocity $v$ through a fluid of viscosity $\eta$ is given by the formula:$F = 6\,\pi \eta \,rv$From this expression,it is clear that the force $F$ is directly proportional to the radius $r$ and the velocity $v$ of the spherical ball.Therefore,the correct option is $B$.

Class 11 Physics Fluid Mechanics and Surface Tension Viscosity and Stoke's Law and Terminal Velocity

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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

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A
Inversely proportional to $r$ but directly proportional to velocity $v$
B
Directly proportional to both radius $r$ and velocity $v$
C
Inversely proportional to both radius $r$ and velocity $v$
D
Directly proportional to $r$ but inversely proportional to $v$

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Fluid Mechanics and Surface Tension

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Viscosity and Stoke's Law and Terminal Velocity

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$A$ small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity-time graph for the transit of the ball?

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Which of the following is the incorrect graph for a sphere falling in a viscous liquid? (Given at $t = 0$,velocity $v = 0$ and displacement $x = 0$.)

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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

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The terminal velocity of a liquid drop of radius $r$ falling through air is $v$. If two such drops are combined to form a bigger drop,the terminal velocity with which the bigger drop falls through air is (ignore any buoyant force due to air).

$A$ solid steel ball of diameter $3.6 \ mm$ acquires a terminal velocity of $2.45 \times 10^{-2} \ m/s$ while falling under gravity through an oil of density $925 \ kg/m^3$. Take the density of steel as $7825 \ kg/m^3$ and $g$ as $9.8 \ m/s^2$. The viscosity of the oil in $SI$ units is:

State Stokes' law. By using it,deduce the expression for:$(i)$ Initial acceleration of a smooth sphere.$(ii)$ Equation of terminal velocity of a sphere falling freely through a viscous medium.$(iii)$ Explain: Upward motion of bubbles produced in a fluid.

$A$ small steel ball is dropped into a long cylinder containing glycerine. Which one of the following is the correct representation of the velocity-time graph for the transit of the ball?

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State Stokes' law. By using it,deduce the expression for:
$(i)$ Initial acceleration of a smooth sphere.
$(ii)$ Equation of terminal velocity of a sphere falling freely through a viscous medium.
$(iii)$ Explain: Upward motion of bubbles produced in a fluid.