Question

the center of gravity of a basketball is located

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at the point of application when balanced
at its geometrical center
at a point opposite to its center of mass
in the material making up its mass
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Explanation:

For a symmetric and homogeneous object like a basketball, the center of gravity coincides with its geometric center. The center of gravity is the point where the weight of the object can be considered to act. Since a basketball has uniform mass - distribution and is symmetric, this point is at its geometric center. The center of mass and center of gravity are the same for objects in a uniform gravitational field, and it is not at a point opposite to the center of mass or just in the material making up its mass in a non - specific way. When balanced, the point of application may be related to the support point but is not the center of gravity.

Answer:

at its geometrical center