The center of mass of a sphere is its geometric center.
The radius of a sphere is equal distance from the center of the sphere to all points within the sphere.
It is the radius of the sphere
A rounded figure that has all surface points equidistant from the center is a sphere. A common object that is a sphere is a tennis ball.
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.
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.
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.
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.
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.
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.
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.