Question

Given a block of wood with a volume of 3.00 ml and a height of 5.00 cm. If 3.50 cm of the block's height are underwater when it floats, then what is the mass of the block in grams?A)0.233 B)2.10 C)5.00 D)17.5 E)1.43

Answer 1

Given,

Voume of the bock of wood,

$V=3.00\text{ ml}$

The height is

$h=5.00cm$

The blocks height under water is

$h^{\prime}=3.50cm$

To find

Mass of the block

Explanation

We have,

Density of water is

$\rho=\frac{1000kg}{m^3}$

We know,

$\begin{gathered} V=Ah \\ \Rightarrow A=\frac{3\times10^{-6}}{5\times10^{-2}}=6.0\times10^{-5}m^3 \end{gathered}$

Thus the new volume is

$\begin{gathered} V^{\prime}=Ah^{\prime} \\ \Rightarrow V^{\prime}=6\times10^{-5}\times3\times10^{-2}=2.1\times10^{-6}m^3 \end{gathered}$

Now we have,

$\begin{gathered} mg=\rho V^{\prime}g \\ \Rightarrow m=1000\times2.1\times10^{-6}_{}=2.1\text{ g} \end{gathered}$

Conclusion

The mass is B.2.1 g