Concept of separation of charges in lightning clouds I have read in an article that when lightning strikes in the clouds the cloud disintegrates into two parts of which the negatively charged part is bigger than the positively charged one. Why does this happen?
Here is the screenshot of that article which is a textbook paragraph.

 A: I think you just missunderstood the textbook article. It says,

There are ice particles in the clouds, which grow, collide, fracture
  and break apart. The smaller particles acquire positive charge and the
  larger ones negative charge.

Not the clouds grow, collide, fracture and break apart, but the ice particles. In fact, the article is a bit simplistic on how this leads to a separation of charges. Upon further research, you'll find that it is highly non-trivial and there seem to be a variety of effects at work. This paper explores them in great detail. One of the major contributions seems to be due to supercooled water:
Updrafts in the thunder cloud transport small droplets of water upwards. As the droplets rise they cool down but cannot freeze yet. They become supercooled. Meanwhile,  big "ice particle", i.e. hail, forms in the cold upper regions of the cloud and falls downwards due to gravity.
When the falling hail collides with the supercooled droplets, the latter freeze instantly, releasing their latent heat to the hail. Thus, the descending hail is always a bit warmer than its environment pushing it towards melting. The hail becomes also supercooled / "soft" and is then referred to as graupel.
Now, when the falling graupel collides with other rising droplets of water, it rips off electrons from the droplet. This site refers to it as a critical phenomenon, in. A more thorough description may be found here. However, as something related to the phase transition and the accompanying supercritical states of matter, it is bound to be complicated.
Bottom line is that the graupel acquires an additional negative charge due to the excess electrons. The droplet which were on their way up are missing it, so the upper part of the cloud is charged positively.
