Question

Q. Two balls A and B of same size are dropped from the same point under Gravity. The mass of A is greater than that of B. If the air resistance acting on each ball is same, then
(1)Both both the balls reach the ground simultaneously
(2)The ball is reaches earlier
(3)The ball B reaches earlier
(4)Nothing can be said

Answer 1

The heavier one will reach the ground first. Note that saying that the air resistance is the same for both is a bit vague, and it is by no means the same thing as neglecting air resistance.
The drag force depends on the shape of an object (surface area) and therefore it is the same for two identical balls with different mass. But the acceleration experienced by the body is inversely proportional to its mass. Thus you have

F =Fg + Fdrag

Now the gravitational force has the very special property of being proportional to the mass of the body itself (Fg=mg) and so the equation of motion is:
y¨=g−Fdrag/mass

As you can see the second term on the right hand side becomes less and less important as the mass of the body is increased, resulting in a larger acceleration. If one neglects air resistance, on the other hand, such term vanishes no matter the value of mm, and so the bodies fall at the same rate as in the experiment performed by Galileo.