Question

Eight spherical rain drops of the same mass and radius are falling down a terminal speed of 6 cms–1. If they coalesce to form one big drop, what will be its terminal speed? Neglect the buoyancy due to air.

Solution

Correct option is

24 cm s–1

 

Let r be the radius of each small drop. The volume of each drop . Let R be the radius of the big drop formed when 8 small drops coalesce. The volume of the big drop will be 8 times that of the small drop. Hence

          

  

  

i.e., the radius of the big drop is twice the radius of each small drop. Now, if the buoyancy of the drop due to air is neglected, the terminal speed of the small drop is given by 

           

The terminal speed of the big drop will be  

            

Dividing (i) and (ii), we have  

        

.

SIMILAR QUESTIONS

Q1

A body floats in water with 40% of its volume outside water. When the same body floats in oil, 60% of its volume remains outside oil. The relative density of oil is  

Q2

The relative density of ice is 0.9 and that of sea water is 1.125. What fraction of the whole volume of an iceberg appears above the surface of the sea?

Q3

A common hydrometer has a uniform stem graduated downwards from 0, 1, 2, ….. up to 10. When floating in pure water it reads 0 and in a liquid of relative density 1.5, it reads 10. What is the relative density of a liquid in which it reads 5?

Q4

A piece of ice, with a stone frozen inside it, is floating in water contained in a beaker. When the ice melts, the level of water in the beaker

Q5

A cubical vessel of height 1 m is full of water. What is the amount of work done is pumping water out of the vessel? Take g = 10ms–2 

Q6

The dimensions of viscosity in terms of M, L and T are

Q7

The dimensions of Reynold’s number are

Q8

A rain drop of radius r falls in air with a terminal speed vt. What is the terminal speed of a rain drop of radius 2r

Q9

Water flows steadily through a horizontal pipe of a variable cross-section. If the pressure of water is p at a point where the velocity of flow is v, what is the pressure at another point where the velocity of flow is 2v being the density of water?    

Q10

The cylindrical tube of a spray pump has a radius R, one end of which hasn fine holes, each of radius r. If the speed of flow of the liquid in the tube is V, the speed of ejection of the liquid through the holes is