1. A liquid rises to a height of 9 cm in a glass capillary with a radius of 0.02 cm. What will be the height of the liquid column in a similar glass capillary with a radius of 0.03 cm?

2. Estimate the capillary depression for mercury in a glass capillary tube with a diameter of 2 mm. Use [tex]\sigma = 0.514 \, \text{N/m}^3[/tex] and [tex]\theta = 140^\circ[/tex].

3. A capillary tube of uniform bore is dipped vertically in water, which rises to 7 cm inside the tube. Find the radius of the capillary if the surface tension is 70 dynes/cm.

The height of a liquid column in a capillary is inversely proportional to the radius of the capillary, according to the capillary action equation:

h = 2σ cos θ / ρgr.

1. We can use the ratio of the radii of the two capillaries to calculate the height of the liquid column in the second capillary. The new height, h2, is given by:

h1*r1 = h2*r2

where h1, r1 are the initial height and radius, and h2, r2 are the final height and radius.

Thus, h2 = (h1*r1)/r2

= (9 cm * 0.02 cm) / 0.03 cm

= 6 cm.

2. To estimate the capillary depression, we utilize the capillary action equation:

h = 2σ cos θ / ρgr.

We know that for mercury,

cos θ = cos 140

= -0.766

ρ ~ 13.6 g/cm³, g ~ 980 cm/sec².

The radius of the capillary r = D/2 = 0.1 cm.

Thus, h = [2*0.514 N*m / (13600 kg*m³ * 9.8 m*s² * 0.001 m)]*100 cm/m

h = -0.75 cm. The minus sign indicates a depression.

3. To find the radius of the capillary, we rearrange the capillary action equation to solve for r:

r = 2σ cos θ / ρgh.

Using a surface tension,

σ = 70 dynes/cm

We get r = 2*70 dynes/cm * cos 0 / (1 g/cm³ * 980 cm/sec <>em²<>/em * 7 cm)

r = 0.02 cm.

Therefore,

The height of the liquid column in the second capillary should be 6 cm.

The capillary depression for mercury in a glass capillary tube 2 mm in diameter should be -0.75 cm.

The radius of the capillary where water rises 7 cm is estimated at 0.02 cm.

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