Question

Why does the location of the center of gravity depend on how an object’s mass is distributed?

Answer 1

Hint : Centre of gravity refers to that point where the total gravitational force acts. We know from Newton’s second law, force is a product of mass times acceleration, so for gravity to act there must be some mass and we know that the centre of mass is defined as that point where the whole mass of the body is supposed to be concentrated. It is not necessary that center of mass and center of gravity coincides.

Complete Step By Step Answer:
The center of mass and the center of gravity coincides for small objects but for an extended object or a body, they may not necessarily coincide. The object is termed as small when the vertical height is very small as compared to the radius of the earth.
It is a well-known fact that the center of gravity shifts towards the side with greater mass and hence the location of the center of gravity of a body depends on the distribution of mass. By distribution of mass we imply the geometry, shape and size of the body.

Note :
Incase of small rigid bodies the position of center of gravity and center of mass is the same and it is the centroid. Sometimes the center of mass doesn't fall anywhere on the object but the center of gravity always falls inside the object. The location of the center of gravity depends upon the gravitational field. In a uniform gravitational field, the centre of gravity is identical to the centre of mass.