Question

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)  

Solution

Correct option is

 

Let R be the radius of the drop and r the radius of each droplet.   

   Volume of one big drop = volume of 64 droplets. 

                                         

.

Increase in surface-area is 

            

                

                

                

                .

 work done W = surface tension  increase in surface area  

                     

                          .

    

  

             .

SIMILAR QUESTIONS

Q1

 

A cubical block of iron 5 cm on each side is floating on mercury in a vessel. Water is poured into the vessel so that it just covers the iron block. What is the height of water column? 

[RD of Hg = 13.6 and Fe = 7.2] 

Q2

A glass beaker having mass 390 g and an interior volume of 500 cm3 floats on water when it is less than half filled with water. What is the density of the material of the beaker?

Q3

 

A block of wood weighs 12 kg and has a relative density 0.6. It is to be in water with 0.9 of its volume immersed. What weight of a metal is needed if the metal is attached below the wood?

[RD of metal = 14]  

Q4

A wooden stick of length L, radius R and density  has a small metal piece of mass m (of negligible volume) attached to its one end. Find the minimum value of the mass m (in terms of given parameters) that would make the stick float vertically in equilibrium in a liquid of density 

Q5

Calculate the rate of flow of glycerine of density  through the conical section of a pipe, if the radii of its ends are 0.1 m and 0.04 m and the pressure drop across its length is 10 N/m2.

Q6

A non-viscous liquid of constant density 1000 kg/m3 flows in a streamline motion along a tube of variable cross-section. The tube is kept inclined in the vertical plane as shown in figure. The area of cross-section of the tube at two points P and Q at heights of 2 metre and 5 metre are respectively  the velocity of the liquid at point P is 1 m/s. Find the work done per unit volume by the pressure and the gravity forces as the fluid flows from point P to Q.     

                                                          

Q7

The fresh water behind a reservoir dam is 15 m deep. A horizontal pipe 4.0 cm in diameter passes through the dam 6.0 m below the water surface as shown in figure. A plug secures the pipe opening. The plug is removed. What volume of water flows out of the pipe in 3.0- hour?     

                                                          

Q8

A soap film is on a rectangular wire ring of size . If the size of the film is changed to , then calculate the work done in this process. The surface tension of soap film is 

Q9

The surface tension of a soap solution is 0.03 N/m. How much work is required to form a bubble of 1.0 cm radius from this solution? 

Q10

 

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?