Question

A piece of wood of dimensions $1\text{m}\times 2\text{m}\times 3\text{m}$ has a mass of $360\text{kg}$. What is the density of wood in ${\text{kg/m}}^3$? Would the wood float in water? ${\rho }_{water}=1000{\text{kg/m}}^3$

• A. $60,$ Yes it will float
• B. $600\times {10}^{-3},$ No it will not float
• C. $60\times {10}^{-3},$ Yes it will float
• D. $600,$ No it will not float

Answer 1

The correct option is A $60,$ Yes it will float

Volume of the wood $=1\text{m}\times 2\text{m}\times 3\text{m}=6{\text{m}}^3$

So, the density of wood $=\frac{\text{Mass of wood}}{\text{Volume of wood}}$

Hence, ${\rho }_{wood}$ $=$ $\frac{360\text{kg}}{6{\text{m}}^3}$ $=$ $60{\text{kg/m}}^3$
Now, to check whether the wood floats or not we need to calculate the relative density with respect to water as a reference material (or specific gravity).

So, relative density $=$ $\frac{60}{1000}=60\times {10}^{-3}$, which is less than $1$.

Hence, the substance is less dense than water and it would float.