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A glass tube of uniform internal radius r has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve.

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Important Questions on Mechanical Properties of Fluids

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A soap bubble having radius of

1 m m

is blown from a detergent solution having a surface tension of

2.5 \times 10^{- 2} N m^{- 1} .

The pressure inside the bubble equals at a point

Z_{0}

below the free surface of water in a container. Taking

g = 10 m s^{- 2},

density of water

= 10^{3} k g m^{- 3},

the value of

Z_{0}

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

Two soap bubbles of radii

3 mm

and

4 mm

confined in vacuum coalesce isothermally to form a new bubble. The radius of the bubble formed

(in mm)

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A glass capillary tube is of the shape of a truncated cone with an apex angle

α

so that its two ends have cross-sections of different radii. When dipped in water vertically, the water rises in it to a height

h

, where the radius of its cross-section is

b

. If the surface tension of water is

S

, its density is

ρ

, and its contact angle with glass is

θ

, then the value of

h

will be (

g

is the acceleration due to gravity)

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MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

Work done in increasing the size of a soap bubble from radius of (

3

5

)

cm

is nearly (surface tension of soap solution

= 0.03 N m^{- 1}

)

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A large number of liquid drops each of radius

r

coalesce to form a single drop of radius

R

. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (Surface tension of liquid

T

, Density

ρ

)

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

Pressure inside two soap bubbles are

1.01

and

1.02

atmosphere, respectively. The ratio of their volumes is :

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A large number of liquid drops each of radius

r

coalesce to form a single drop of the radius

R

. The energy released in the process is converted into kinetic energy of the big drop so formed. The speed of the big drop is (given surface tension of the liquid

T

, density

ρ

)

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A large number of water drops, each of radius

r

, combine to have a drop of radius

R

. If the surface tension is

T

and mechanical equivalent of heat is

J

, the rise in heat energy per unit volume will be:

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

Two mercury drops (each of radius

r

) merge to form a bigger drop. The surface energy of the bigger drop, if

T

is the surface tension, is

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A big water drop is formed by the combination of

n

small water drops of equal radii. The ratio of the surface energy of

n

drops to the surface energy of the big drop is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

Two separate soap bubbles of radii

3 \times 10^{- 3} m

and

2 \times 10^{- 3} m

respectively, formed of same liquid (surface tension

65 \times 10^{- 2} N m^{- 1}

) come together to form a double bubble. The radius of interface of double bubble is

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by:

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EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

The surface tension of the soap water solution is

\frac{1}{10 π} N m^{- 1}

. The free energy of the surface layer of a soap bubble of diameter

5 mm

will be

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A certain number of spherical drops of a liquid of radius

r

coalesce to form a single drop of radius

R

and volume

V .

T

is the surface tension of the liquid then:

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

Two small drops of mercury each of radius

R

coalesce to form a large single drop. The ratio of the total surface energies before and after the change is

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

When two soap bubbles of radii

a

and

b

(b > a)

coalesce, the radius of curvature of common surface is:

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A soap bubble of radius

R

is blown. After heating the solution, a second bubble of radius

2 R

is blown. The work required to blow the second bubble in comparison to that required for the first bubble is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A soap bubble of radius

r

is blown up to form a bubble of radius

2 r

under isothermal conditions. If

σ

is the surface tension of the soap solution, the energy spent in the process is

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A small soap bubble of radius 4cm is trapped inside another bubble of radius 6cm without any contact. Let

P_{2}

be the pressure inside the inner bubble and

P_{0}

, the pressure outside the outer bubble. Radius of another bubble with pressure difference

P_{2} - P_{0}

between its inside and outside would be:

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Surface Tension

A soap bubble, blown by a mechanical pump at the mouth of a tube increases in volume with time at a constant rate. The graph that correctly depicts the time dependence of pressure inside the bubble is given by:

A glass tube of uniform internal radius r has a valve separating the two identical ends. Initially, the valve is in a tightly closed position. End 1 has a hemispherical soap bubble of radius r. End 2 has sub-hemispherical soap bubble as shown in figure. Just after opening the valve.

Important Questions on Mechanical Properties of Fluids

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