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Q: Where is center of mass of a sphere?

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

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.

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!).

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.

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.

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.

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.

The the center of the donut , more specifically the center of the hole of the donut. Considering the donut is perfectly symmetrical we only need to look at the geometric center of it , same applies for a hollow sphere like a soccer ball ,the center is indeed in the middle where there is no mass.

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.

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.

"The center of the universe" doesn't make sense. Imagine a sphere where the surface of the sphere can be compared to our universe. Where is the center of the skin? It is impossible to answer, as any point on the sphere is identical to any other. You might say that the center is inside the sphere, but remember, the universe is akin to the surface of the sphere only, not the whole sphere.

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.

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