Chapter 8, Problem 1TC

The three metal balls are held suspended and submerged in water. Rank the buoyant force on each from greatest to least.

Solution

To determine: The rank of the buoyant force from greatest to least.

Answer:

The rank of buoyant force from greatest to least is $C>B>A$.

Explanation:

Given Info: The volume of the metal ball A is $25{\text{cm}}^{\text{3}}$ , the volume of metal ball is $60{\text{cm}}^{\text{3}}$ and the volume of metal ball C is $120{\text{cm}}^{\text{3}}$ .

Write the expression for buoyancy force.

$F=V\rho g$

Here,

$\rho$ is density of the ball

$V$ is the volume of the ball

$g$ is the acceleration due to gravity

From above expression, the relation between buoyancy force and volume of the ball is shown below.

$F\propto V$

The value of buoyancy force depends upon the volume of the ball. The volume of ball C is more that the volume of ball A and B.

Conclusion:

Therefore, the rank of buoyant force from greatest to least is $C>B>A$ .