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The center of mass of a sphere is its geometric center.

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Q: Where is center of mass of a sphere?
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Can centre of mass of a body can exist at point where there is no mass of the object?

Yes. For example, the center of mass of a hollow sphere would be at the empty center of that sphere.

Is center of gravity lies where there is no mass?

That all depends on the shape of the object and how its mass is distributed. The center of gravity of a solid sphere is at the center of the solid sphere. The center of gravity of a solid cube is at the center of the solid cube. The Earth's center of gravity is at the center of the Earth, and there's certainly plenty of mass there. But the center of gravity of a ring is at the center of the ring ... an open space where the finger goes.

Center of mass of Earth's atmosphere?

Assuming that the Earth's atmosphere is a perfect sphere, then the atmosphere's center of mass will be at the point equidistant between Earth's poles (i.e. the center of the Earth!).

When the force of gravity is calculated using a large spherically symmetric mass like the Earth the distance is measured to the centre of the sphere why is this so?

Teh force of gravity is measured form the center of gravity, thus the center of gravity of the object is appropriately the center of the force. The center of the sphere is also the center of gravity of the sphere.

What is meant by the term center of gravity?

It's an older term; nowadays the phrase "Center of mass" seems to be preferred. It's, basically, the mass-weighted center of a ... well, a thing. The center of a sphere of uniform density is easy to calculate; it's the geometric center of the sphere. For other shapes or for objects where the density is not the same throughout, it's more complicated.

How does the centre of gravity change as the size of the object changes?

The location of an object's center of gravity depends on the object's shape, and on how its mass is distributed throughout its shape, but not on its size. The center of gravity of a homogeneous sphere is at the center of the sphere, no matter whether the sphere's radius is 1 millimeter or 1 light year.

Is the mass the same as a diametre?

No. Mass is the weight of an object. Diameter is the distance from one side of a circle or sphere to the other side passing through the center.

What is the difference between equator and Equator?

An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass; whereas, the capitalized term Equator refers to the Earth's equator.

What will be centre of gravity of sphere full of water and it is leaking?

If the sphere of water remains a sphere as it leaks, and the water leaving the boundary of the sphere are no longer considered part of the sphere, the center of gravity will be the center of sphere. If the sphere does not have to remain a sphere as it leaks, if it was in a spherical container, the center of gravity would move downward from center, approaching the source of leakage.

Is the center of a great circle also the center of a small circle?

No. Every circle on the sphere whose center is also the center of the sphere is a great circle. If the circle's center is not also the center of the sphere, then the circle is a small circle.

What is the formula for the mass of a sphere?

The mass of a sphere is 4/3*pi*r3*d where r is the radius of the sphere and d is the density of the material of the sphere.

Is the center of gravity located in the center of objects made of like material?

Only objects that have the exact size, shape, mass and density distribution can have the same center of mass. Any variation and the center of gravity would move. Furthermore, only objects that are geometrically symmetrical (think sphere) can have a center of gravity at their geometric center.