Question

In fluid statics, the line of action of the buoyant force always acts through the

• A. centre of gravity of any submerged body
• B. centroid of the volume of any floating body
• C. centroid of the displaced volume of fluid by the body
• D. centroid of the volume of fluid vertically above the body

Hint:

The buoyant force acts through the centroid of the displaced fluid, which is why the body's stability in water depends on the position of its center of gravity and the centroid of displaced fluid.

Answer 1

The Correct Option is C

In fluid statics, the buoyant force is the force exerted on a submerged or floating body due to the pressure difference in the fluid. The line of action of the buoyant force always passes through the centroid of the displaced fluid. This is a fundamental principle known as Archimedes' principle. 
Step 1: Understanding Buoyant Force 
According to Archimedes' principle, the buoyant force is equal to the weight of the displaced fluid, and it acts vertically upward. The force's line of action passes through the centroid of the displaced fluid. Therefore, the correct answer is (C). 
Final Answer: \[ \boxed{\text{(C) centroid of the displaced volume of fluid by the body}} \]