a tube of 0.8mm radius is dipp.ed into a liquid with surface tension and density 6/100 N/m and 900 kg/m3.if 5he tube is kept vertical the height of liquid risen in it will be

To determine how high the liquid will rise in a tube with a given radius when it is dipped into a liquid with surface tension, we can use the concept of capillarity. The height to which a liquid rises in a capillary tube can be calculated using the formula derived from the principles of surface tension and gravity.

Understanding Capillary Rise

Capillary action occurs when the adhesive forces between the liquid and the walls of the tube are stronger than the cohesive forces within the liquid itself. This phenomenon is particularly noticeable in narrow tubes, like the one you mentioned with a radius of 0.8 mm.

The Formula for Capillary Rise

The height \( h \) to which the liquid rises in the tube can be calculated using the formula:

h = (2 * γ) / (ρ * g * r)

• γ = surface tension of the liquid (in N/m)
• ρ = density of the liquid (in kg/m³)
• g = acceleration due to gravity (approximately 9.81 m/s²)
• r = radius of the tube (in meters)

Plugging in the Values

Now, let’s substitute the values you provided into the formula:

• Surface tension, \( γ = 6/100 \, \text{N/m} = 0.06 \, \text{N/m} \)
• Density, \( ρ = 900 \, \text{kg/m}³ \)
• Radius, \( r = 0.8 \, \text{mm} = 0.0008 \, \text{m} \)
• Acceleration due to gravity, \( g = 9.81 \, \text{m/s}² \)

Now, substituting these values into the formula:

h = (2 * 0.06) / (900 * 9.81 * 0.0008)

Calculating the Height

Let’s do the math step-by-step:

• Calculate the numerator: \( 2 * 0.06 = 0.12 \, \text{N/m} \)
• Calculate the denominator: \( 900 * 9.81 * 0.0008 = 7.0656 \, \text{N/m} \)

Now, divide the numerator by the denominator:

h = 0.12 / 7.0656 ≈ 0.017 \, \text{m}

Final Result

Converting meters to centimeters (since 1 m = 100 cm), we find:

h ≈ 1.7 \, \text{cm}

Therefore, the height of the liquid that rises in the tube is approximately 1.7 cm. This example illustrates how surface tension and the dimensions of the tube interact to influence the behavior of liquids in narrow spaces.