Question

If Earth exerts a gravitational force on the moon, why doesn't the moon fall into the Earth?
Also write what happens to the gravitational force between any two objects when
(a) mass of one of the object increases
(b) distance between the object increases.

Answer 1

The pull between the earth and the moon depends on basically two factors, the masses of the celestial bodies and the distance between them.
The moon does not fall and collide with the Earth because of the fact that it has velocity that is nearly perpendicular to the pull from the Earth.
The moon's velocity and distance from Earth allow it to make a perfect balance between fall and escape.
If the moon were moving in a perfect circle, the gravitational force would always be "sideways" and just cause it to change its direction.

(a) If the mass of one of the object increases, gravitational force between them also increases.
(b) If the distance between the object increases, gravitational force between them decreases.