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Mechanical Properties of Fluids

Multiple Choice Questions

71.
Two small drops of mercury, each of radius R, coalesce to form a single large drop. The ratio of the total surface energies before and after change is

1 : 2^1/3

2^1/3 : 1

2 : 1

1 : 2

2^1/3 : 1

Radius of one drop of mercury is R

∴ The volume of one drop = $\frac{4}{3} π R^{3}$

∴ Total volume of the two drops,

V = 2 × $\frac{4}{3} π R^{3}$

V = $\frac{8}{3} {πR}^{3}$

Let the radius of the large drop formed be R'

The total volume of the large is also V

$\frac{4}{3} π R'^{2} = \frac{8}{3} π R^{3}$

R'³ = 2R³

⇒ R' = 2^1/3 R

Now the surface area of the resultant drop is

S₁= 2 × 4 $π$ R²

S₁= 8 $π$ R²

and the surface area of the resultant drop is

S₂ = 4 $π$ R'²

S₂ = 4 $π$ 2^2/3R²

Let T be the surface tension of the mercury. Therefore the surface energy of the two drops before coalescing is

U₁ = S₁ T

U₁= 8 $π$ R²T

and the surface energy after coalescing,

U₂ = S₂T

U₂= 2^2/3 × 4 $π$ R²T

∴ $\frac{U_{1}}{U_{2}} = \frac{8 π R^{2} T}{2^{\frac{2}{3}} \times 4 π R^{2} T}$

= $\frac{2}{2^{\frac{2}{3}}}$

$\frac{U_{1}}{U_{2}}$ = 2^1/3

72.

Scent sprayer is based on

Charle's law
Archimedes principle
Boyle's law
Bernoulli's theorem

73.

The property utilized in the manufacture of lead shots is

specific weight of liquid lead
compressibility of liquid lead
specific gravity of liquid lead
surface tension of liquid lead

74.

Assertion: Thin films such a soap bubble or a thin layer of oil on water show beautiful colours when illuminated by white light.

Reason: It happens due to the interference of light reflected from upper surface of the thin film.

If both the assertion and reason are true and reason is a correct explanation of assertion.
If both assertion and reason are true but assertion is not a correct explanation of the assertion.
If both the assertion is true but the reason is false.
If both assertion and reason are false.

75.

For liquid to rise in a capillary tube, the angle of contact should be

acute
obtuse
right
none of these

76.

Which of the following physical wuantity do not have same dimensions?

pressure and stress
tension and surface tension
strain and angle
energy and work

77.

The length of a needle floating on water is 2.5 cm. Calculate the added force (due to surface tension) required to pull the needle out of water. (Surface tension of water = 7.2 $\times$ 10^-2 N/m²)

3.6 $\times$ 10^-3 N
3.4 $\times$ 10^-10 N
3.0 $\times$ 10^-5 N
3.8 $\times$ 10^-11 N

78.

A capillary tube of radius r is immersed in water and water rises in it to a height H. Mass of water in the capillary tube is m. If the capillary of radius 2r is taken and dipped in water, the mass of water that will rise in the capillary tube will be

79.

The work done in increasing the size of a soap film from 10 cm x 6 cm to 10 cm x 11 cm is 3 x 10^-4 J. The surface tension of the film is

1.5 × 10^-2 N/m
3 × 10^-2 N/m
6.0 × 10^-2 N/m
11 × 10^-2 N/m

80.

The maximum force in addition to the weight required to pull a wire 5.0 cm long from the surface of the water at temperature 20°C, is 728 dyne. The surface tension of water is

7.28 N/cm
7.28 dyne/cm
72.8 dyne/cm
7.28 × 10² dyne/cm

Previous Year Papers

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Multiple Choice Questions

71. Two small drops of mercury, each of radius R, coalesce to form a single large drop. The ratio of the total surface energies before and after change is 1 : 21/3 21/3 : 1 2 : 1 1 : 2

71.
Two small drops of mercury, each of radius R, coalesce to form a single large drop. The ratio of the total surface energies before and after change is

1 : 2^1/3

2^1/3 : 1

2 : 1

1 : 2