Question

Small air bubbles rises slowly as compared to bigger ones .why?

Answer 1

There are two kinds of forces act on the bubble inside the liquid:

1) Weight in the downward direction
2) Upthrust due to the displaced liquid in the upward direction

Now, Large bubbles rise faster.
The force is provided by the displacement of water, therefore the larger the amount of air the larger the force, so they rise faster.

Answer 2

assume a spherical bubble (I always wanted to say that) of radius r. 

Its force of buoyancy is a function of its volume (ie, ~r³, and its force of drag is a function of its cross-sectional area and the square of its speed (ie, ~r²v²). Terminal velocity (ie, constant velocity) is reached when force of buoyancy equals force of drag, or r³ = r²v². 

So, using this simplified math, for a bubble with a radius r = 1, 

1³ = 1²v², or 1 = v²

and so v = 1. 

For a larger bubble of radius r = 2, 

2³ = 2²v², or 8 = 4v², or 2 = v²

and so v² = 2, or v = √2 = 1.414... 

So, actually, larger bubbles should rise faster than smaller ones, the speed being proportional to the square root of its radius. Assuming spherical bubbles, of course. 

You can also simplify the original equation, r³ = r²v², down to r = v², or v = √r, which shows the relationship more clearly.