If a ball is thrown upwards from the surface of the earth then initially
a)The earth remains stationary while the ball moves upwards
b)The ball remains stationary while the earth moves downwards
c)The ball and earth both move toward each other
d)The ball and earth both move away from each other
Also explain why and how
The Earth is attracted to the ball because of gravity. This force is attractive regardless of the motion direction. When the ball flies upwards, the Earth is still attracted upwards by Fg→g.
When you through the ball upwards, then we are looking at another phenomenon: Newton's 3rd law. The push Fp→p upwards on the ball implies a downwards push Fp→p on the Earth.
Whichever of these two forces Fp→p and Fg→g have the largest influence, determine the resulting motion and direction of the Earth (this is Newton's 2nd law).