1. If a capillary tube with a diameter of 1 mm is inserted into water, what will be the capillary rise in the tube?

2. If a capillary rise of 4 cm is observed in a capillary tube when the tube is inserted into water, calculate the diameter of the tube.

3. A capillary tube of 2 mm is inserted into a 3-liter liquid with a mass of 5 kg. What will be the capillary rise in the tube if the surface tension is 0.12 N/m?

4. A capillary rise of 45 mm is observed when a capillary tube is inserted into a liquid with a specific weight of 9 kN/m$^3$. What will be the radius of the capillary tube if the surface tension of the liquid is 0.12 N/m?

1. The capillary rise is given by the formula: h = (2T cos θ) / ρgr where h is the capillary rise, T is the surface tension of water, θ is the angle of contact between the capillary tube and water, ρ is the density of water, and r is the radius of the capillary tube.

Substituting the values of T, θ, ρ, and r, we get:h = (2 x 0.0728 x cos 0°) / (1000 x 9.8 x 0.0005) = 29.63 mm (approximately)

2. If a capillary rise of 4 cm is noticed in a capillary tube when the tube is inserted into water, calculate the diameter of the tube.

The capillary rise is given by the formula: h = (2T cos θ) / ρgrwhere h is the capillary rise, T is the surface tension of water, θ is the angle of contact between the capillary tube and water, ρ is the density of water, and r is the radius of the capillary tube.

Rearranging the above equation, we get:r = sqrt(2T cos θ / ρg h)Diameter of the capillary tube = 2r.Substituting the values of T, θ, ρ, and h, we get:r = sqrt(2 x 0.0728 x cos 0° / (1000 x 9.8 x 0.04)) = 0.125 mm

3. The capillary rise is given by the formula: h = (2T cos θ) / ρgrwhere h is the capillary rise, T is the surface tension of water, θ is the angle of contact between the capillary tube and water, ρ is the density of water, and r is the radius of the capillary tube.Substituting the values of T, θ, ρ, and r, we get:h = (2 x 0.12 x cos 0°) / (1000 x 9.8 x 0.002) = 12.24 mm

4. The capillary rise is given by the formula: h = (2T cos θ) / ρgrwhere h is the capillary rise, T is the surface tension of water, θ is the angle of contact between the capillary tube and water, ρ is the density of water, and r is the radius of the capillary tube.

Rearranging the above equation, we get:r = sqrt(2T cos θ / ρg h)Substituting the values of T, θ, ρ, and h, we get:r = sqrt(2 x 0.12 x cos 0° / (9000 x 9.8 x 0.045)) = 0.087 mm (approximately)

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