Question

You are provided with a hollow iron ball of volume $20c{m}^3$ and of mass $15g$ and a solid iron ball of mass $20g$ having the same volume. Both are placed on the surface of water containing in a large tube. Which will float? Give reasons for your answer.

Answer 1

Step 1: Given data

The volume of hollow ball, ${\mathit{V}}_{\mathbf{h}}\mathbf{=}\mathbf{20}\mathbf{}\mathit{c}{\mathit{m}}^{\mathbf{3}}$

Mass of hollow ball, ${\mathit{M}}_{\mathbf{h}}\mathbf{=}\mathbf{15}\mathbf{}\mathit{g}$

Mass of solid iron ball, ${\mathit{M}}_{\mathbf{i}}\mathbf{=}\mathbf{20}\mathbf{}\mathit{g}$

The density of iron, $\mathit{d}\mathbf{=}\mathbf{8}\mathit{g}\mathbf{/}\mathit{c}{\mathit{m}}^{\mathbf{3}}$

Step 2: Finding the density of the hollow iron ball

Density$\mathbf{=}\frac{\mathbf{M}\mathbf{a}\mathbf{s}\mathbf{s}}{\mathbf{V}\mathbf{o}\mathbf{l}\mathbf{u}\mathbf{m}\mathbf{e}}$

The density of hollow iron ball $\mathbf{=}\frac{{\mathbf{M}}_{\mathbf{h}}}{{\mathbf{V}}_{\mathbf{h}}}$

$$\begin{gathered} {\mathit{d}}_{\mathbf{h}}\mathbf{=}\frac{\mathbf{15}}{\mathbf{20}} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{75}\mathbf{}\mathit{g}\mathbf{/}\mathit{c}{\mathit{m}}^{\mathbf{3}} \end{gathered}$$

A hollow iron ball will float in water because its density is less than that of water, which is $\mathbf{1}\mathbf{}\mathit{g}\mathbf{/}\mathit{c}{\mathit{m}}^{\mathbf{3}}\mathbf{.}$
The density of a solid iron ball is $\mathbf{8}\mathbf{}\mathit{g}\mathbf{/}\mathit{c}{\mathit{m}}^{\mathbf{3}}$. It will sink because its density is greater than that of water.