object B moves
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An object, in itself, does not have any force. It can exert a force on another object, such as gravitational or electro-magnetic attraction or repulsion, or from impact. However, in all such cases, you require two (or more) objects: one object, in isolation, exerts no force.
Yes, when the object is submerged in water then water exerts opposite buoyonci force which decrease the weight of object.
Mass is the amount of matter in an object. It does not change based on gravity. Weight is the force an object exerts 'downward' due to gravitational acceleration. Force = (mass)*(acceleration). Acceleration due to gravity is less on the Moon than on Earth.
Object B must be circumscribed about object A.
.Object B must be inscribed in object A.