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. 1000 cm³B. 2 cm³C. 9.8 cm³D. 2000 cm3

Answer 1

Given:

The mass of the ball is m = 2000 g

The density of water is

$\rho=1\text{ g/cm}^3$

To find the minimum volume of the ball that could have without sinking.

Explanation:

The condition for the ball to float is

$\begin{gathered} Weight\text{ of the ball = buoyant force} \\ mg=V\rho g \end{gathered}$

Here, g is the acceleration due to gravity.

V is the minimum volume of the ball.

On substituting the values, the volume of the ball will be

$\begin{gathered} m=V\rho \\ V=\frac{m}{\rho} \\ =\frac{2000g}{1\text{ g/cm}^3} \\ =\text{ 2000 cm}^3 \end{gathered}$

Thus, the minimum volume that the ball could have without sinking below the surface of the water is 2000 cm^3