Why do bigger water particles acquire negative charge? In clouds, smaller water particles acquire positive charge and bigger water particles acquire negetive charge, why?
Sometimes, large amounts of charges get accumulated in the lower part of clouds and induce an opposite charge on earth, why is it. Why does it induce an opposite charge and how?
 A: Thunderstorms are obviously areas of turbulent and chaotic atmospheric activity. There are updraughts and downdraughts moving rapidly in opposite directions within regions adjacent to each other. This has the net effect of lifting the smaller, lighter droplets to the top of the clouds and the larger,  more massive  droplets to the base of the cloud.   
Simultaneously, frozen material in the former of ice and hail particles are carried downwards, hitting off of the larger water droplets already at the base of the clouds. This collision process results in the freezing of the water droplets and the release of heat. 
This additional heat acts to produce a mushy outer layer of the falling hail and sleet.  This called  "soft hail", aka graupel, hits water droplets, and  it results in the transfer of electrons from the smaller uplifted water droplets and the electrons accumulate on the falling,  more massive particles.
Source: Electron Transfer within Clouds

As it gathers moisture, the sphere becomes larger and heavier. Eventually it reaches a critical mass, and gravity begins to pull it toward the ground. As it falls, it collides with other graupel rising in the updrafts. Scientists believe that this is the mechanism that generates the electrical charge inside thunderstorms. The cool graupel, and the cold air falling with it, rubs against the warm graupel and the warm air rising with it, "grabbing" electrons in the process. Graupel continues to rise and fall within the cloud, polarizing it further with each successive trip. This electron transfer leads to a layered electrical charge in the cloud. The faster a storm builds, the more suspended particles will collide and the greater the electrical charge will be. 

You end up with a cloud that has a positive charge on the top and a negative charge at the base.
Beneath the cloud, especially in the lower altitude, this negative charge  cloud base induces a positively charged ground electrical field, which the photo below illustrates. 

Source:  Illustration of Electric Field. 
This picture is included  in my physics textbook and shows the effect of a strong electrical field. A few minutes after the picture was taken, lighting struck the viewing platform, killing one man and badly burning a boy.
This produces lightning strikes at ground level, although around 3/4 of the discharges remain within the cloud. 
