Chapter 19, Problem 17A

Does the buoyant force on a floating object depend on the weight of the object itself or on the weight of the fluid displaced by the object? Or are these both the same for the special case of floating?

To determine

Whether the buoyant force depends on the weight of the floating object or weight of the fluid displaced by the object.

Explanation of Solution

Introduction:

When an object is placed in a fluid, the fluid exerts a pressure on the object. This pressure acting on an object will create a force that will try to lift the object. This pressure acting per unit area of the object is called buoyancy force.

This buoyancy force acting on an object is expressed as follows

  $\begin{array}{l}P=\frac{F_b}{A}=\rho gh\\ F_b=\rho ghA\\ F_b=\rho gV\text{ (}\because hA=V\text{)}\end{array}$

Where,

  $\rho$ = density of fluid

  $g$ = acceleration due to gravity

  $A$ = area of cross-section of the object

  $V$ = volume of the fluid displaced

According to this, when an object immersed in a fluid, the weight of the fluid displaced will be equal to the weight of the object.

This is true only when the object is floating.

If the object is heavier, then it will completely sink. The weight of displaced fluid will not be equal to the weight of the object.

Conclusion:

The buoyancy force depends on the weight of displaced water that will be equal to weight of the object only when the object is floating in water. When the object sinks completely in the fluid, these two weights will not be equal to each other.