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Spherical ball of radius $r$ is 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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Important Questions on Mechanical Properties of Fluids

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

Eight drops of water, each of radius

2 m m

are falling through air at a terminal velocity of

8 c m s^{- 1}

. If they coalesce to from a single drop, then the terminal velocity of combined drop will be:

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

What will be the approximate terminal velocity of a rain drop of diameter

1.8 \times 10^{- 3} m

, when density of rain water

\approx 10^{3} {kgm}^{- 3}

and the coefficient of viscosity of air

\approx 1.8 \times 10^{- 5} N - sm

^{- 2} ?

(Neglect buoyancy of air)

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

Two solid spheres of the same metal but of mass

M

and

8 M

fall simultaneously in a viscous liquid. The ratio of terminal velocity of the second sphere to that of the first sphere is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

Under a constant pressure head, the rate of flow of orderly volume flow of liquid through a capillary tube is

V .

if the length of the capillary is doubled and the diameter of the bore is halved, the rate of flow would become

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

In an experiment to verify Stokes 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)

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

The velocity of rain drop having radius

1 mm

20 cm s^{- 1}

. The velocity of raindrops of size

3 mm

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

Which of the following diagrams correctly shows the relation between the terminal velocity

v_{T}

of a spherical body falling in a liquid and viscosity

η

of the liquid?

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

An air bubble of radius

1.0 cm

rises with a constant speed of

3.5 mm s^{- 1}

through a liquid of density

1.75 \times 10^{3} kg m^{- 3} .

Neglecting the density of air. the coefficient of viscosity of the liquid is _________

{kgm}^{- 1} s^{- 1}

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

A rain drop of radius

0.3 mm

has a terminal velocity in air of

1 m s^{- 1}

. The viscosity of air is

8 \times 10^{- 5}

poise. The viscous force on it is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

Two rain drops falling through air have radii in the ratio

1 : 2

. They will have terminal velocity in the ratio

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

A metallic spherical ball of mass

M

is dropped into a liquid and after some time it reaches a terminal velocity of

v

. If another spherical ball of mass

8 M

made of the same metal is dropped into the same liquid, then its terminal velocity will be (assume the spheres to be uniformly dense)

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

Which of the following option correctly describes the variation of the speed

υ

and acceleration 'a' of a point mass falling vertically in a viscous medium that applies a force

F = - k υ

, where 'k' is a constant, on the body? (Graphs are schematic and not drown to scale)

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

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 : [Density of water $f_{w} = 1000 kg m^{- 3}$ and Density of air $f_{a} = 1.2 kg m^{- 3}, g = 10 m / s^{2}$ Coefficient of viscosity of air $= 1.8 \times 10^{- 5} N s m^{- 2}]$

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

A tiny spherical oil drop carrying a net charge

q

is balanced in still air with a vertical uniform electric field of strength

\frac{81 π}{7} \times 10^{5} V m^{- 1}

. When the field is switched off, the drop is observed to fall with terminal velocity

2 \times 10^{- 3} m s^{- 1}

. Given,

g = 9.8 m s^{- 2}

, the viscosity of the air

= 1.8 \times 10^{- 5} N s m^{- 2}

, and the density of the oil

= 900 kg m^{- 3}

, the magnitude of

q

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius

2.0 \times 10^{- 5} m

and density

1.2 \times 10^{3} kg m^{- 3}

? Take viscosity of liquid

= 1.8 \times 10^{- 5} N s m^{- 2} .

(Neglect buoyancy due to air).

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

Two rain drops falling through air have radii in the ratio

1 : 2

. They will have terminal velocity in the ratio________

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

What is the terminal velocity of air bubble of

1.0 mm

in diameter rising in liquid of viscosity

0.85 N - s m^{- 2}

and density

900 kg m^{- 3}

?(air density

1.293 kg m^{- 3}, g = 9 m s^{- 2}]

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

A small spherical body of radius $r$ and density $ρ$ moves with the terminal velocity $v$ in a fluid of coefficient of viscosity $η$ and density $σ .$ What will be the net force on the body?

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

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

(\frac{v_{1}}{v_{2}})

equals:

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Stokes Law

Two tubes of radii

r_{1}

and

r_{2}

and lengths

l_{1}

and

l_{2,}

respectively, are connected in series and a liquid flows through each of them in stream line conditions.

P_{1}

and

P_{2}

are pressure differences across the two tubes. If

P_{2}

4 P_{1}

and

l_{2}

\frac{l_{1}}{4}

then the radius

r_{2}

will be equal to :

Spherical ball of radius r is falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball is

Important Questions on Mechanical Properties of Fluids

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Spherical ball of radius $r$ is falling in a viscous fluid of viscosity $η$ with a velocity $v$ . The retarding viscous force acting on the spherical ball is