Viscosity and Stokes' Law

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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

R

but inversely proportional to

v

(B)

directly proportional to both radius

R

and velocity

v

(C)

inversely proportional to both radius

R

and velocity

v

(D)

inversely proportional to

R

but directly proportional to velocity

v

LEVELJEE Main

A spherical solid ball of volume $V$ is made of a material of density $ρ_{1}$ . It is falling through a liquid of density $ρ_{2} (ρ_{2} < ρ_{1})$ . [Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$ , i.e., $F_{viscous} = - k v^{2} (k > 0)$ ]. The terminal speed of the ball is

(A)

\frac{V g ( ρ _{1} - ρ _{2} )}{k}

(B)

\frac{V g ρ _{1}}{k}

(C)

\frac{V g ρ _{1}}{k}

(D)

\frac{V g ( ρ _{1} - ρ _{2} )}{k}

JEE Main 2021

LEVELJEE Main

A raindrop with radius $R = 0.2 mm$ falls from a cloud at a height $h = 2000 m$ above the ground. Assume that, the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is (Take, density of water, $ρ_{w} = 1000 kg m^{- 3}$ and density of air, $ρ_{a} = 1.2 kg m^{- 3}$ , $g = 10 m/s^{2}$ , coefficient of viscosity of air, $η = 1.8 \times 1 0^{- 5} N-s m^{- 2}$ )

(A)

250.6 ms^{- 1}

(B)

43.56 ms^{- 1}

(C)

4.94 ms^{- 1}

(D)

14.4 ms^{- 1}

JEE Main 2006

LEVELJEE Main

If the terminal speed of a sphere of gold (density = $19.5 kgm^{- 3}$ ) is $0.2 ms^{- 1}$ in a viscous liquid (density = $1.5 kgm^{- 3}$ ), find the terminal speed of a sphere of silver (density = $10.5 kg/m^{3}$ ) of the same size in the same liquid.

(A)

0.4 ms^{- 1}

(B)

0.133 ms^{- 1}

(C)

0.1 ms^{- 1}

(D)

0.2 ms^{- 1}

JEE Main 2020

LEVELJEE Main

In an experiment to verify Stoke's law, a small spherical ball of radius $r$ and density $ρ$ falls under gravity through a distance $h$ in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of $h$ is proportional to (Ignore viscosity of air)

(A)

r^{4}

(B)

r

(C)

r^{3}

(D)

r^{2}

JEE Main 2021

LEVELJEE Main

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius $2.0 \times 1 0^{- 5}$ m and density $1.2 \times 1 0^{3} kgm^{- 3}$ ? Take viscosity of liquid $= 1.8 \times 1 0^{- 5} Nsm^{- 2}$ . (Neglect buoyancy due to air).

(A)

3.8 \times 1 0^{- 11} N

(B)

3.9 \times 1 0^{- 10} N

(C)

1.8 \times 1 0^{- 10} N

(D)

5.8 \times 1 0^{- 10} N

JEE Main 2019

LEVELJEE Main

A solid sphere of radius $R$ acquires a terminal velocity $v_{1}$ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity $η$ . The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, $v_{2}$ when falling through the same fluid, the ratio $(v_{1} / v_{2})$ equals

(A)

(B)

\frac{1}{27}

(C)

\frac{1}{9}

(D)

JEE Advanced 2016

LEVELJEE Main

Consider two solid spheres P and Q each of density $8 gm cm^{- 3}$ and diameters $1 cm$ and $0.5 cm$ , respectively. Sphere P is dropped into a liquid of density $0.8 gm cm^{- 3}$ and viscosity $η = 3 poiseulles$ . Sphere Q is dropped into a liquid of density $1.6 gm cm^{- 3}$ and viscosity $η = 2 poiseulles$ . The ratio of the terminal velocities of P and Q is

JEE Advanced 2003

LEVELJEE Advanced

A liquid of density $900 kg/m^{3}$ is filled in a cylindrical tank of upper radius $0.9 m$ and lower radius $0.3 m$ . A capillary tube of length $l$ is attached at the bottom of the tank as shown in the figure. The capillary has outer radius $0.002 m$ and inner radius $a$ . When pressure $p$ is applied at the top of the tank volume flow rate of the liquid is $8 \times 1 0^{- 6} m^{3} /s$ and if capillary tube is detached, the liquid comes out from the tank with a velocity $10 m/s$ . Determine the coefficient of viscosity of the liquid. [Given, $π a^{2} = 1 0^{- 6} m^{2}$ and $a^{2} / l = 2 \times 1 0^{- 6} m$ ]

JEE Advanced 2018

LEVELJEE Main

Consider a thin square plate floating on a viscous liquid in a large tank. The height $h$ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity $u_{0}$ . Which of the following statements is (are) true?

* Multiple Correct Options

(A)

The resistive force of liquid on the plate is inversely proportional to

h

(B)

The resistive force of liquid on the plate is independent of the area of the plate

(C)

The tangential (shear) stress on the floor of the tank increases with

u_{0}

(D)

The tangential (shear) stress on the plate varies linearly with the viscosity

η

of the liquid

JEE Advanced 2015

LEVELJEE Advanced

Two spheres $P$ and $Q$ of equal radii have densities $ρ_{1}$ and $ρ_{2}$ , respectively. The spheres are connected by a massless string and placed in liquids $L_{1}$ and $L_{2}$ of densities $σ_{1}$ and $σ_{2}$ and viscosities $η_{1}$ and $η_{2}$ , respectively. They float in equilibrium with the sphere $P$ in $L_{1}$ and sphere $Q$ in $L_{2}$ and the string being taut (see figure). If sphere $P$ alone in $L_{2}$ has terminal velocity $v_{P}$ and $Q$ alone in $L_{1}$ has terminal velocity $v_{Q}$ , then

* Multiple Correct Options

(A)

\frac{v _{P}}{v _{Q}} = \frac{η _{1}}{η _{2}}

(B)

\frac{v _{P}}{v _{Q}} = \frac{η _{2}}{η _{1}}

(C)

v_{P} \cdot v_{Q} > 0

(D)

v_{P} \cdot v_{Q} < 0

JEE Advanced 2004

LEVELJEE Advanced

A small sphere falls from rest in a viscous liquid. Due to friction, heat is produced. Find the relation between the rate of production of heat and the radius of the sphere at terminal velocity.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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

A small sphere falls from rest in a viscous liquid. Due to friction, heat is produced. Find the relation between the rate of production of heat and the radius of the sphere at terminal velocity.

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