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? 


Correct option is


The work done in making a bubble by blowing is stored in the form of energy in the surface of the bubble. The soap bubble has surfaces, external and internal. The ar5ea of both the surface is 


where r is the radius of the bubble. Here



  work done = energy of the extended area

                      = surface tension  area  






A large block of ice 5 m thick has a vertical hole drilled through it floating in the middle of a lake. What is the minimum length of a rope required to scoop up a bucket full of water through the hole?

[RD of ice = 0.9]




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] 


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?



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]  


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 


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.


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.     



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?     



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 


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)