Question

If the relative density of a solid is 1.2, then 12 g of that substance will occupy 10 \[{m^3}\].
A. True
B. False

Answer 1

Hint: First we know that the density of any material equals the mass of the material divided by its volume. Whereas the relative density is the ratio between the density (mass of a unit volume) of a measuring substance and the density of some other reference substance (typically water) at a given temperature and it is unitless. Then using the relative density formula check if the given statement is true or false.

Complete step by step answer:
Given relative density of the substance \[ = 1.2\], mass of the substance (\[m\])\[ = 12\;g\] and let \[v\] be its volume. We know that the density of water is \[1\;g/c{m^3}\]. Since,
\[\text{Relative density} = \dfrac{\text{Density of substance}}{\text{Density of water}}\]
Hence the density of substance is \[1.2\;g/c{m^3}\]
We also know that \[Density = \dfrac{{Mass}}{{Volume}}\]
\[Density = \dfrac{m}{v}\]---(1)
Substitute the values of density and mass in the equation (1), we get
\[1.2\;g/c{m^3} = \dfrac{{12\;g}}{v}\]
\[ \Rightarrow v = \dfrac{{12}}{{1.2}}c{m^3}\]
\[ \Rightarrow v = 10\;c{m^3}\]----(2)
Since we know that \[1\;cm = {10^{ - 2}}m\], then the equation (2) becomes
\[\therefore v = 10 \times {10^{ - 6}}{m^3}\].
​So the given statement is false.

Hence option B is correct.

Note: If we don't know the density of water we are not able to solve this type of questions. In this question the reference substance is not specified, so we take water as a reference substance. Also note that the density of a substance is the same regardless of the size of the sample.