$K g / m^{3}$ and $g / c m^{3}$ are units of density and $1000 k g / m^{3} = 1 g / c m^{3}$ . By following the rule $N_{1} U_{1} = N_{2} U_{2}$ . We can say that $k g / m^{3}$ is a smaller unit, when compared to $g / c m^{3}$

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1000 k g / m^{3} = 1 g / c m^{3} i s w r o n g

Statement is correct but it does not follow the rule

N \propto \frac{1}{U}

No,

N_{1} U_{1} = N_{2} U_{2}

is not applicable to density

Yes, the statement is true and it follows the rule

N \propto \frac{1}{U}

answer is B.

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Detailed Solution

\frac{1 k g}{m^{3}} = \frac{1000 g}{10^{6} c m^{3}}

$= \frac{10^{3}}{10^{6}} \frac{g}{c m^{3}}$

$= \frac{1}{10^{3}} g / c m^{3}$

$10^{3} k g / m^{3} = 1 g / c m^{3}$

It follow rule $N \propto \frac{1}{U}$

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