Question

A ball with a mass of 2000 g is floating on the surface of a pool of water.What is the minimum volume that the ball could have without sinking belowthe surface of the water? (Note that water has a density of 1.00 g/cm3.)A. 200 cm3B. 2000 cm3C. 9.8 cm3D. 1,000 cm3

Answer 1

B. 2,000 cm³

Step-by-step explanation

Given:

• The mass of the ball, m = 2000 g

,

• The density of water, ρ = 1.00 g/cm³

Find:

• The minimum volume that the ball could have without sinking below the surface of the water, V

There are two forces acting on the ball: the buoyant force, and the weight of the ball,

If the buoyant force is greater than or equal to the object's weight, then the object will float. If the buoyant force is less than the weight, then the object will sink under the surface.

So we have,

`F_b=F_g`

Replace the forces with their expressions,

`\rho_(water)\cdot g\cdot V_{submerged\text{ }ball}=m\cdot g`

Solving for the volume of the submerged part of the ball,

`V_{submerged\text{ }ball}=(m)/(\rho_(water))=(2000g)/(1.00g/cm^3)=2000\text{ }cm^3`

If the ball has a volume of 2,000 cm³, it will be totally submerged in the water. For any volume above that value, the ball will have a part of its volume above the surface of the water.

Hence, the minimum value that the ball could have is 2,000 cm³.