Chapter SH, Problem 17.7APP

To determine

To calculate:The density of the bolt in ${\text{g/cm}}^{\text{3}}$ .

Answer to Problem 17.7APP

The density of the metal bolt is $7.6{\text{ g/cm}}^3$ .

Explanation of Solution

Given data:

Mass of the metal bolt $=26.6\text{ g}$

Initial volume of water in the $\text{50-mL}$ graduated cylinder $=27.0\text{ mL}$

Final volume of water in the cylinder $=30.5\text{ mL}$

Formula used:

Density of any substance,

  $\text{density}=\frac{\text{mass}}{\text{volume}}$

Calculation:

As per the problem,

Mass of the metal bolt $=26.6\text{ g}$

Initial volume of water in the cylinder $=27.0\text{ mL}$

Final volume of water in the cylinder $=30.5\text{ mL}$

Volume of the metal bolt is equal to the change in volume of water in the cylinder.

Change in volume of water in the cylinder

  $\begin{array}{l}=V_{final}-V_{initial}\\ =30.5\text{ mL}-27.0\text{ mL}\\ =\text{3}\text{.5 mL}\end{array}$

So, volume of the metal bolt $=\text{3}\text{.5 mL}=\text{3}{\text{.5 cm}}^3\text{ [1mL}=1{\text{ cm}}^3]$

Substitute the values of mass and volume of bolt in the density formula to finditsdensity. $\begin{array}{l}\text{density}=\frac{\text{mass }}{\text{volume}}\\ \text{density}=\frac{\text{26}\text{.6 g}}{\text{3}{\text{.5 cm}}^3}\\ =7.6{\text{ g/cm}}^3\end{array}$

Conclusion:

The density of the metal bolt is $7.6{\text{ g/cm}}^3$ .