Question

A mercury drop of radius 1 cm is sprayed into 106 droplets of equal size. Calculate the energy expended if surface tension of mercury* is .

Solution

Correct option is

 

If a drop of radius R is sprayed into n droplets of equal radius r, then as a drop has only one surface, the initial surface area will be  while final area . So the increase in area

        

So energy expended in the process.  

          

Now since the total volume of n droplets is the same as that of initial drop, i.e.,  

           

So substituting the value of r from eq. (ii) in (i), 

            

So here,  

       

            .

SIMILAR QUESTIONS

Q1

Find the velocity of glycerine (having density 1.3 g/cc) if a steel ball of 2 mm radius (density = 8 g/cc) acquires a terminal velocity of 4 cm/s in falling freely in the tank of glycerine.

Q2

An area bubble of radius 1mm is allowed to rise through a long cylindrical column of a viscous liquid of radius 5 cm and travels at a steady rate of 2.1 cm per sec. If the density of the liquid is 1.47 g per cc, find its velocity. Assume g = 980 cm/sec2 and neglect the density of air.

Q3

Two equal drops of water are falling through air with a steady velocity v. If the drops coalesced, what will be the new velocity.

Q4

A spherical ball of radius  and 104 kg/m3 falls freely under gravity through a distance h before entering a tank of water. If after entering the water the velocity of the ball does not change, find h. The viscosity of water is .

Q5

Water flows through a capillary tube of radius r and length l at a rate of 40 ml per second, when connected to a pressure difference of h cm of water. Another tube of the same length but radius r/2 is connected in series with this tube and the combination is connected to the same pressure head. Calculate the pressure difference across each tube and the rate of flow of water through the combination.  

Q6

 

Spherical particles of pollen are shaken up in water and allowed to settle. The depth of the water is . What is the diameter of largest particles remaining in suspension on hour later?

   

Q7

A cylindrical vessel of area of cross-section and filled with liquid to a height of h1 has a capillary tube of length 1 and radius r protruding horizontally at its bottom. If the viscosity of liquid is , density  and g = 9.8 m/s2, find the time in which the level of water in vessel falls to h2.

Q8

Vessel whose bottom has round holes with diameter of 1 mm is filled with water. Assuming that surface tension acts only at holes, find the maximum height to which the water can filled in the vessel without leakage. Given that surface tension of water is 

Q9

A ring is cut from a platinum tube of 8.5 cm internal and 8.7 cm external diameter. It is supported horizontally from a pan of a balance so that it comes in contact with the water in a glass vessel. What is the surface tension of water is an extra 3.97 g weight is required to pull it away from water? (g = 980 cm/s2)

                                                                

Q10

The lower end of a capillary tube of diameter 2.00 mm is dipped 8.00 cm below the surface of water in a beaker. What is the pressure required in the tube to blow a bubble at its end in water? Also calculate the excess pressure. [Surface tension of water  density of water = 103kg/m3, 1 atmosphere