हिंदी

Find the Height to Which the Same Water Will Rise in Another Glass Capillary Having Half Area of Cross Section.

Advertisements
Advertisements

प्रश्न

Water rises to a height 3.2 cm in a glass capillary tube. Find the height to which the same water will rise in another glass capillary having half area of cross section.

संख्यात्मक
Advertisements

उत्तर

`h_1` = 3.2cm, `A_2 = (A_1)/2`

As, `h  α  1/r`

`therefore h_1r_1 = h_2r_2`

`pir_2^2 = (pir_1^2)/2`

`=> r_2 = (r_1)/sqrt2`

`therefore h_2 = (3.2 xx r_1)/(r_1//sqrt2) = 3.2 xx sqrt2`

Hence, `h_2 = 4.525` cm

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2013-2014 (October)

APPEARS IN

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Define the angle of contact.


Explain why Surface tension of a liquid is independent of the area of the surface


Fill in the blanks using the word(s) from the list appended with each statement

Surface tension of liquids generally . . . with temperatures (increases / decreases)


A U-shaped wire is dipped in a soap solution and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5 × 10–2 N (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film?


The total energy of free surface of a liquid drop is 2π times the surface tension of the liquid. What is the diameter of the drop? (Assume all terms in SI unit).


Show that the surface tension of a liquid is numerically equal to the surface energy per unit
area.


When a sparingly soluble substance like alcohol is dissolved in water, surface tension of water


The free surface of a liquid resting in an inertial frame is horizontal. Does the normal to the free surface pass through the centre of the earth? Think separately if the liquid is (a) at the equator (b) at a pole (c) somewhere else.


If a mosquito is dipped into water and released, it is not able to fly till it is dry again. Explain 


When the size of a soap bubble is increased by pushing more air in it, the surface area increases. Does it mean that the average separation between the surface molecules is increased?

 

By a surface of a liquid we mean


Air is pushed into a soap bubble of radius r to double its radius. If the surface tension of the soap solution in S, the work done in the process is 


If more air is pushed in a soap bubble, the pressure in it


If two soap bubbles of different radii are connected by a tube,


Which of the following graphs may represent the relation between the capillary rise hand the radius r of the capillary?


Water rises in a vertical capillary tube up to a length of 10 cm. If the tube is inclined at 45°, the length of water risen in the tube will be


The rise of a liquid in a capillary tube depends on

(a) the material
(b) the length
(c) the outer radius
(d) the inner radius of the tube


Find the excess pressure inside (a) a drop of mercury of radius 2 mm (b) a soap bubble of radius 4 mm and (c) an air bubble of radius 4 mm formed inside a tank of water. Surface tension of mercury, soap solution and water are 0.465 N m−1, 0.03 N m−1 and 0.076 N m−1 respectively.


Consider a small surface area of 1 mm2 at the top of a mercury drop of radius 4.0 mm. Find the force exerted on this area (a) by the air above it (b) by the mercury below it and (c) by the mercury surface in contact with it. Atmospheric pressure = 1.0 × 105 Pa and surface tension of mercury = 0.465 N m−1.  Neglect the effect of gravity. Assume all numbers to be exact.


A barometer is constructed with its tube having radius 1.0 mm. Assume that the surface of mercury in the tube is spherical in shape. If the atmospheric pressure is equal to 76 cm of mercury, what will be the height raised in the barometer tube? The contact angle of mercury with glass = 135° and surface tension of mercury = 0.465 N m−1. Density of mercury = 13600 kg m−3


A capillary tube of radius 0.50 mm is dipped vertically in a pot of water. Find the difference between the pressure of the water in the tube 5.0 cm below the surface and the atmospheric pressure. Surface tension of water = 0.075 N m−1.


The lower end of a capillary tube of radius 1 mm is dipped vertically into mercury. (a) Find the depression of mercury column in the capillary. (b) If the length dipped inside is half the answer of part (a), find the angle made by the mercury surface at the end of the capillary with the vertical. Surface tension of mercury = 0.465 N m−1 and the contact angle of mercury with glass −135 °.


Two large glass plates are placed vertically and parallel to each other inside a tank of water with separation between the plates equal to 1 mm. Find the rise of water in the space between the plates. Surface tension of water = 0.075 Nm−1.


Find the force exerted by the water on a 2 m2 plane surface of a large stone placed at the bottom of a sea 500 m deep. Does the force depend on the orientation of the surface?


A cubical block of ice floating in water has to support a metal piece weighing 0.5 kg. Water can be the minimum edge of the block so that it does not sink in water? Specific gravity of ice = 0.9. 


A hollow spherical body of inner and outer radii 6 cm and 8 cm respectively floats half-submerged in water. Find the density of the material of the sphere.


The energy stored in a soap bubble of diameter 6 cm and T = 0.04 N/m is nearly ______.


How much amount of work is done in forming a soap bubble of radius r?


The water droplets are spherical in free fall due to ______ 


Define surface tension.


Two soap bubbles have a radius in the ratio of 2:3. Compare the works done in blowing these bubbles.  


Numerical Problem.

A stone weighs 500 N. Calculate the pressure exerted by it if it makes contact with a surface of area 25 cm2.


Distinguish between cohesive and adhesive forces.


What are the factors affecting the surface tension of a liquid?


What do you mean by capillarity or capillary action?


A drop of oil placed on the surface of water spreads out. But a drop of water place on oil contracts to a spherical shape. Why?


What is capillarity?


Two spherical rain drops reach the surface of the earth with terminal velocities having ratio 16 : 9. The ratio of their surface area is ______.


The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of the water column and 'h' is the height of water in the capillary. The inner circumference of the capillary is ______.

(surface tension of water = 7 × 10-2 N/m)


Under isothermal conditions, two soap bubbles of radii 'r1' and 'r2' coalesce to form a big drop. The radius of the big drop is ______.


Soap solution is used for cleaning dirty clothes because ______.


What is surface tension? Explain the applications of surface tension.


For a surface molecule ______.

  1. the net force on it is zero.
  2. there is a net downward force.
  3. the potential energy is less than that of a molecule inside.
  4. the potential energy is more than that of a molecule inside.

Surface tension is exhibited by liquids due to force of attraction between molecules of the liquid. The surface tension decreases with increase in temperature and vanishes at boiling point. Given that the latent heat of vaporisation for water Lv = 540 k cal kg–1, the mechanical equivalent of heat J = 4.2 J cal–1, density of water ρw = 103 kg l–1, Avagadro’s No NA = 6.0 × 1026 k mole–1 and the molecular weight of water MA = 18 kg for 1 k mole.

  1. Estimate the energy required for one molecule of water to evaporate.
  2. Show that the inter–molecular distance for water is `d = [M_A/N_A xx 1/ρ_w]^(1/3)` and find its value.
  3. 1 g of water in the vapor state at 1 atm occupies 1601 cm3. Estimate the intermolecular distance at boiling point, in the vapour state.
  4. During vaporisation a molecule overcomes a force F, assumed constant, to go from an inter-molecular distance d to d ′. Estimate the value of F.
  5. Calculate F/d, which is a measure of the surface tension.

A hot air balloon is a sphere of radius 8 m. The air inside is at a temperature of 60°C. How large a mass can the balloon lift when the outside temperature is 20°C? (Assume air is an ideal gas, R = 8.314 J mole–1K–1, 1 atm. = 1.013 × 105 Pa; the membrane tension is 5 Nm–1.)


A soap bubble of radius 3 cm is formed inside another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is ______ cm.


We have three identical perfectly black plates. The temperatures of first and third plate is T and 3T. What is the temperature of second plate if system is in equilibrium?


In a U-tube, the radii of two columns are respectively r1 and r2. When a liquid of density ρ(θ = 0°) is filled in it, a level difference of h is observed on two arms, then the surface tension of the liquid is ______.


The excess pressure inside a liquid drop is 500 Nm-2. If the radius of the drop is 2 mm, the surface tension of the liquid is x × 10-3 Nm-1. The value of x is ______.


A soap film of surface tension 3 × 10-2 formed in a rectangular frame can support a straw as shown in Fig. If g = 10 ms-12, the mass of the straw is ______.


The surface tension of soap solution is 25 × 10-3 Nm-1. The excess of pressure inside a soap bubble of diameter 1 cm is ______.


Calculate (i) the pressure due to the weight of the water at a depth of 2.5 m and (ii) the depth below the surface of water at which the pressure due to the weight of the water equals 1.0 atm.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×