MEDIUM

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A cylinder of mass $M$ and radius $R$ moves with constant speed $v$ through a region of space that contains dust particles of mass $m$ which are at rest. There are $n$ number of particles per unit volume. The cylinder moves in a direction perpendicular to its axis. Assume $m < < M$ and that the particles do not interact with each other. All the collisions taking place are perfectly elastic and the surface of the cylinder is smooth. The drag force per unit length of the cylinder required to maintain a speed $v$ constant for the cylinder when it has entered a region is $\frac{K}{3} n m R v^{2}$ . Find the value of $K$ .

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Important Questions on Fluid Dynamics

MEDIUM

Physics>Mechanical Properties of Matter>Fluid Dynamics>Viscosity

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>Fluid Dynamics>Viscosity

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>Fluid Dynamics>Viscosity

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>Fluid Dynamics>Viscosity

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

MEDIUM

Physics>Mechanical Properties of Matter>Fluid Dynamics>Viscosity

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:

EASY

Physics>Mechanical Properties of Matter>Fluid Dynamics>Viscosity

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>Fluid Dynamics>Viscosity

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)

EASY

Physics>Mechanical Properties of Matter>Fluid Dynamics>Viscosity

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}

EASY

Physics>Mechanical Properties of Matter>Fluid Dynamics>Viscosity

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)

MEDIUM

Physics>Mechanical Properties of Matter>Fluid Dynamics>Viscosity

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

HARD

Physics>Mechanical Properties of Matter>Fluid Dynamics>Viscosity

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>Fluid Dynamics>Viscosity

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>Fluid Dynamics>Viscosity

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>Fluid Dynamics>Viscosity

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>Fluid Dynamics>Viscosity

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>Fluid Dynamics>Viscosity

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>Fluid Dynamics>Viscosity

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>Fluid Dynamics>Viscosity

Two rain drops falling through air have radii in the ratio

1 : 2

. They will have terminal velocity in the ratio

MEDIUM

Physics>Mechanical Properties of Matter>Fluid Dynamics>Viscosity

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:

HARD

Physics>Mechanical Properties of Matter>Fluid Dynamics>Viscosity

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 :

Important Questions on Fluid Dynamics

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