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. $600\times {10}^{-3},$ No
• B. $600,$ No
• C. $60\times {10}^{-3},$ Yes
• D. $60,$ Yes

Answer 1

The correct option is D $60,$ Yes

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

So, the density of wood = $\frac{Massofwood}{Volumeofwood}$

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.