Chapter 19, Problem 52A

A 13.5-kg block of metal displaces 5 liters of water when submerged. What kind of metal is likely to compose the block?

To determine

Kind of metal that the block is composed of.

Answer to Problem 52A

The metal block is likely to be composed of aluminum as $\rho =2700{\text{kg/m}}^3$ .

Explanation of Solution

Given:

Mass of metal block, $m=13.5\text{kg}$

Volume of block, $V=5\text{liter}$

Formula Used:

The density is given as,

  $\rho =\frac{m}{V}$

Where, $m$ is mass and $V$ is volume.

Calculation:

The volume in m³ is,

  $V=5\times {10}^{-3}{\text{m}}^3$

So, the density of block is

  $\begin{array}{l}\rho =\frac{13.5\text{kg}}{5\times {10}^{-3}{\text{m}}^3}\\ =2700{\text{kg/m}}^3\end{array}$

Since the density is $\rho =2700{\text{kg/m}}^3$ which is equal to the density of aluminum.

So the metal block is likely to be composed of aluminum.

Conclusion:

Therefore, the metal block is likely to be composed of aluminum as $\rho =2700{\text{kg/m}}^3$ .