Question

A piece of wood has dimensions $1m\times 2m\times 3m$ and a mass of $2kg$. What is the density of wood and will the piece float in water?

$[{\rho }_{water}$ = 1000 $kg{m}^{-3}]$

• A. $0.33kg{m}^{-3}$, Yes
• B. $0.33\times {10}^{-3}kg{m}^{-3}$, No
• C. $3kg{m}^{-3}$, Yes
• D. $3\times {10}^{-3}kg{m}^{-3}$, No

Answer 1

The correct option is A

$0.33kg{m}^{-3}$, Yes

Volume of the piece of wood $=1\times 2\times 3=6m^3$

Mass of the wooden piece $=2kg$
So, the density of the wooden piece $=\frac{\text{mass of the piece}}{\text{volume of the piece}}$
Hence, ${\rho }_{wood}=\frac{2}{6}=0.33kg{m}^{-3}$
Now, to check whether the wooden piece floats or not, we need to compare the density of wood with respect to water. If the density of wood is less than that of water, it will float, else sink. Here, the density of wood is less than that of water. Therefore, it will float.