Which statements are true about the weight of an object and the buoyant force exerted on that object when it is placed in a fluid?

A) They work in opposite directions.
B) They are always equal in strength.
C) They determine whether an object floats or sinks.

A and C

Statement B) They are always equal in strength. is true about the weight of an object and the buoyant force exerted on that object when it is placed in a fluid.

To determine which statements are true about the weight of an object and the buoyant force exerted on that object when it is placed in a fluid, let's analyze each statement:

A) They work in opposite directions.
The statement "They work in opposite directions" is true. The weight of an object acts downward, towards the center of the Earth, while the buoyant force acts upward, opposite to the direction of the weight. This is a result of Archimedes' principle.

B) They are always equal in strength.
The statement "They are always equal in strength" is not true. The weight of an object is determined by the gravitational force acting on it, which depends on the mass of the object and the acceleration due to gravity. The buoyant force, on the other hand, is determined by the density of the fluid and the volume of the object submerged in the fluid. These two forces can be equal when an object is fully submerged or floating at equilibrium, but they can also have different strengths depending on the specific conditions.

C) They determine whether an object floats or sinks.
The statement "They determine whether an object floats or sinks" is true. When an object is placed in a fluid, the balance between its weight and the buoyant force determines its buoyancy. If the weight of the object is greater than the buoyant force, the object sinks. If the buoyant force is greater than the weight, the object floats. When the weight and buoyant force are equal, the object is neutrally buoyant and remains suspended in the fluid without sinking or floating.

In conclusion, the correct statements are:
- A) They work in opposite directions.
- C) They determine whether an object floats or sinks.