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Physics Mechanical Properties of Fluids

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2 months ago

Physics Mechanical Properties of Fluids Class 11th

When a long glass capillary tube of radius 0.015 cm is dipped in a liquid, the liquid rises to a height of 15 cm within it. If the contact angle between the liquid and glass to close to 0°, the surface tension of the liquid, in milli Newton m?¹, is [ρ(liquid) = 900kgm?³, g = 10 ms?²] (Give answer in closest integer)

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alok kumar singh

Contributor-Level 10

The height of capillary rise is given by the formula:
h = (2T cosθ) / (rρg)
Given: h = 15 cm = 0.15 m, r = 0.015 cm = 1.5 * 10? m, ρ = 900 kg/m ³, g = 10 m/s², and θ ≈ 0° (so cosθ ≈ 1).
We need to find the surface tension, T.
T = (h r ρ g) / (2 cosθ)
T = (0.15 * 1.5 * 10? * 900 * 10) / 2
T = 0.10125 N/m
The answer is required in milliNewton m? ¹, so we multiply by 1000.
T = 101.25 mN/m.

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Physics Mechanical Properties of Fluids Class 11th

Pressure inside two soap bubbles are 1.01 and 1.02 atmosphere, respectively. The ratio of their volumes is

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alok kumar singh

Contributor-Level 10

The excess pressure inside a soap bubble is given by ΔP = 4T/R, where T is the surface tension and R is the radius.
The pressures are given as P? = 1.01 atm and P? = 1.02 atm. Let the atmospheric pressure be P? = 1 atm.
ΔP? = P? - P? = 1.01 - 1 = 0.01 atm = 4T/R?
ΔP? = P? - P? = 1.02 - 1 = 0.02 atm = 4T/R?
Dividing the two equations: (ΔP? /ΔP? ) = (R? /R? )
0.01 / 0.02 = R? /R? ⇒ R? /R? = 2
The ratio of their volumes is V? /V? = ( (4/3)πR? ³ ) / ( (4/3)πR? ³ ) = (R? /R? )³ = 2³ = 8.
The ratio is 8:1.

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2 months ago

Physics Mechanical Properties of Fluids Class 11th

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is 5 cm and the angular speed of rotation is ω rads⁻¹. The difference in the height, h (in cm) of liquid at the centre of vessel and at the will be:

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alok kumar singh

Contributor-Level 10

ρdrω²r = ρgdh
ω²∫? rdr = g∫? dh
ω²R²/2 = gh
h = ω²R²/2g = 25ω²/2g

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2 months ago

Physics Mechanical Properties of Fluids Mechanical Properties of Fluids

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)

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Vishal Baghel

Contributor-Level 10

√2gh = (2r²g/9η) (ρ_t - ρ)
⇒ h = (2/81) (r? g (ρ_t - ρ)²/η²)
⇒ h ∝ r?
After falling through h, the velocity be equal to terminal velocity.

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Physics Mechanical Properties of Fluids Class 11th

A leak proof cylinder of length $1 m$ , made of a metal which has very low coefficient of expansion is floating vertically in water at $0^{?} C$ $^{}$ such that its height above the water surface is $20 c m$ . When the temperature of water is increased to $4^{?} C$ $^{}$ , the height of the cylinder above the water surface becomes $21 c m$ . The density of water at $T = 4^{?} C$ $^{}$ , relative to the density at $T = 0^{?} C$ $^{}$ is close to: