Surface Tension chapter numerical for jee main zero to advance level
Type A. Numerical on Surface Tension
1. Calculate the force required to take away a flat plate of radius 5 cm from the surface of water. Given, surface tension of water = 72 dyne cm^-1.
[Ans. 2 , 261.95 dynel
2. A soap film is formed in a rectangular frame of length 7 cm dipping into soap solution. The framework hangs from the arm of a balance. An extra weight of 0.38 g must be placed in the opposite arm to balance the pull of the film. Calculate the surface tension of soap solution.
[Ans. 26.6 dyne cm^-1]
3. A glass plate of length 10 cm, breadth 1.54 cm and thickness 0.2 cm weighs 8.2 g in air. If it is held vertically with long side horizontal and the plate half immersed in water, what will be its apparent weight? Surface tension of water = 73 dyne cm^-1.
[Ans. 8.18 gf]
Type B. Numerical on Surface energy
4. Calculate the work done in blowing a soap bubble from a radius of 2 cm to 3 cm, the surface tension of the soap solution is 30 dyne cm^-1.
[Ans. 3 , 769.9 erg]
5. Calculate the amount of energy evolved, when 8 droplets of water (surface tension 72 dyne cm^-1) of radius 0.5 mm each combine into one.
[Ans. 9.05 erg]
6. Calculate the energy spent in spraying a drop of mercury of 1 cm radius into 10^6 droplets all of same size. Surface tension of mercury is 35 × 10^-3 N/m
Ans. 4.354 × 10 ^-3
7. Find the work done in breaking a spherical drop of 1 mm radius of water into one million droplets. Surface tension of water is 72 dyne cm
[Ans. 895.73 erg]
8. A film of water is formed between two straight-parallel wires each 10 cm long and at separation 0.5 cm. Calculate the work required to increase 1 mm distance between the wires Surface tension of water 72 × 10 ^-3 N/m
[Ans. 1.44×10^-5]
9. A soap bubble is blown to a diameter of 7 cm. If 36,960 erg of work is done in blowing it further, find the new radius The surface tension of soap solution is 40 dyne/cm
[Ans. 7 cm]
Type C. Numerical on Excess of pressure inside a liquid drop and bubble
10. Calculate the excess of pressure inside (a) a drop of liquid of radius 0.2 cm and (b) a bubble of liquid of radius 0.3 cm Given that surface tension of liquid is 24 dyne/cm
[Ans. (0) 240 dyne/cm^2 (b) 320 dyne/cm^2
11. The air pressure inside a soap bubble of diameter 7 mm is 0.8 cm of water column above the atmosphere. Calculate surface tension of soap solution.
[Ans. 68.6 dyne/cm]
12. If the excess pressure inside a soap bubble of radius 1 cm is balanced by a column of oil 3 mm high, find the surface tension of the bubble (Specific gravity of liquid 1.8)
[Ans. 132.3 dyne/cm]
13. What should be the pressure inside a small air bubble of 0.1 mm radius situated just below the free surface of water ? Surface tension of water 72 dyne/cm and atmospheric pressure is 1.013 x 10^6 dyne/cm^2
[Ans. 1.0274 x 10^6 dyne/cm]
14. Two soap bubbles have radii in the ratio 1:2. Compare the excess of pressure inside these bubbles. Also compare the work done in blowing these bubbles.
[Ans. 2:1 ; 1:4]
15. Find the difference in excess pressure on the inside and outside of a rain drop, if its diameter changes from 1.003 cm to 1.002 cm by evaporation. Surface tension of rain water is 72 dyne/cm.
[Ans. 0.14 dyne/cm^2]
Type D. Numerical on Ascent formula
16. Calculate the height to which water at 4°C will rise in a capillary tube of 1 mm diameter. Take g is 980 cm/s^2 and surface tension of water = 72 dyne/cm.
[Ans. 2.94 cm)
17. In an experiment to determine the surface tension of water by capillary rise, in a capillary tube of diameter 10 m, water rises to a height of 0.03 m. Calculate the surface tension of water. Given, g = 9.8 m/s^2, density of water = 1,000 kg/ m^3.
[Ans. 0.0735 N/m]
18. A tube of a mercury barometer is 4.5 mm in diameter. What error does surface tension introduce in its reading ? Given that angle of contact between mercury and glass is 130° and the surface tension is 540 dyne/cm. Take density of mercury as 13.6 g cm and g is 980 cm/s^2
[Ans. 0.2315 cm (less reading)]
19. A capillary tube of inner diameter 0.5 mm is dipped in a liquid of specific gravity 13.6, surface tension 545 dyne/cm, angle of contact 130°. Find the depression or elevation of liquid in the tube.
[Ans. 2-103 cm (depression)]
20. Water rises to a height of 10 cm in a certain capillary tube. If in the same tube, level of mercury is depressed by 3.42 cm, compare the surface tensions of water and mercury Specific gravity of mercury is 13.6, the angle of contact for water is 0° and that for mercury is 135°.
[Ans. 0.152]
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