Centre of mass and centre of gravity?

Question

We know that CM lies inside or outside the body. Can centre of gravity lie outside the body?
where does the CM & CG lie in (a) crescent (b) uniform circular ring?

Answer 1

The center of gravity and center of mass can ALMOST be considered synonymous. The same constraints that apply to the center of mass apply to the center of gravity.

In the real world, the center of gravity will rarely be exactly in the center of mass. The Earth's gravitational field follows the shape of the Earth, meaning it's spherical. If you had a bar perpendicular to a line between the center of the Earth and the bar's center of mass, the ends of the bar would be in a slightly weaker part of the Earth's gravity field than the center of mass. That would place the center of gravity slightly higher than the center of mass.

This is something spacecraft have to consider, since it causes spacecraft to eventually line up their major axis with the Earth's radius if nothing is done to counter it (we don't notice this as much near the surface of the Earth since the effects of the atmosphere are much stronger than the torques caused by the difference between the center of mass and center of gravity).

For the ring, both the center of mass and center of gravity lie at or near the middle of the ring, which is outside the body. Gravity decreases by the inverse square law, the so center of gravity depends on how the ring is oriented relative to the gravity field. If the ring lies in the same plane as the Earth's radius, the center of gravity is slightly below the center of mass. The pull of gravity is stronger on the bottom half of the ring than the top. If the plane of the ring is perpendicular to the Earth's radius, the center of mass would be slightly above the center of mass.

For the crescent, it depends how the mass is distributed. A thin crescent could have both the center of mass and the center of gravity outside the body. A fat crescent that tapers quickly to a point could have both inside the body.

Answer 2

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RE:
Centre of mass and centre of gravity?
We know that CM lies inside or outside the body. Can centre of gravity lie outside the body?
where does the CM & CG lie in (a) crescent (b) uniform circular ring?

Answer 3

--CM and CG are not synonymous.
--CG of a body is the point where the vector sum of gravitational forces on all its particles acts
--CM of a body is that point along which when an external force is applied than the body will react to the force in the same manner as a point object of same mass would behave(if point mass is possible)
--CM and CG coincides only if the acceleration due to gravity acting on all the particles of the body have same value.
--for a very large object, at every point of which acceleration due to gravity is not exactly same, than CM and CG does not coincide.
--Both CM as well as CG gravity may lie inside or outside the body depending upon the distribution of masses in the body.

Answer 4

Center of mass equals center of gravity = M
Gravity acts on each molecule. The sum of all these vectors starts at M. Any other point introduces rotation.
M can be outside the body. Think of a ring.

Th

Answer 5

so can we say from above that CM and CG for high mountains dont coincide