Question

Two capillary tubes of diameters 5.0 mm and 4.0 mm are held vertically inside water one by one. How much high the water will rise in each tube? (g = 9.8 N kg–1, surface tension of water )

Solution

Correct option is

7.1 mm

 

Height of water-column in a capillary of radius r is given by   

           

where T is surface tension,  is density and  is angle of contact of water-glass which can be assumed 0 (cos 0 = 1). 

For the first tube, r = 3.5 mm = 2.5  10–3 m. 

           .  

According to eq. (i), for the same liquid, we have       

        .

If a liquid rises to a height h1 in a capillary of radius r1 and to a height h2in a capillary of radius r2, then

        

    

             .

SIMILAR QUESTIONS

Q1

A mercury drop of radius 1.0 mm breaks up into 64 droplets of equal volumes. Calculate the work done in this process. (Surface tension is mercury is 0.465 N/m)  

Q2

 

A big drop is formed by coalesing 1000 small droplets of water. What will be the change in surface energy? 

What will be the ratio between the total surface energy of the droplets and the surface energy of the big drop?

Q3

 joule work is being done in breaking a big drop of water of radius R into 1000 small drops of equal size. Find out the surface tension of water.

Q4

A drop of mercury has a radius of 3.00 mm at room temperature. The surface tension of mercury at that temperature is 0.465 Nm–1. Find excess pressure inside the drop and the total pressure inside the drop. The atmospheric pressure is .

Q5

What is the excess pressure in a soap bubble of radius 5.00 mm at 20oC? The surface tension of soap solution at 20oC is .

Q6

 

If an air bubble of same radius be formed at a depth of 40.0 cm in a soap solution (relative density 1.20), then what will be the pressure inside the air bubble?

Q7

Two spherical soap bubbles of different radii coalesce. If V is the consequent change in volume of the contained air, and S the change in the total surface area, then show that 3PV + 4ST = 0, where T is surface tension of the soap solution.       

Q8

The limbs of a manometer consist of uniform capillary tubes of radii . Find out the pressure difference if the level of the liquid (density 103 kg/m3, surface tension ) in the narrower tube stands 0.2 m above that in the broader tube. 

Q9

Two separate air bubble (radii 0.002 m and 0.004 m) formed of the same liquid (surface tension 0.07 N/m) come together to form a double. Find the radius and the sense of curvature of two internal film surface common to both the bubbles.  

Q10

Water rises in a capillary tube to a height 2.0 cm. In an another capillary whose radius is one-third of it, how much the water will rise? If the first capillary is inclined at an angle of 60o with the vertical then what will be the position of water in the tube?