# The density of material in SI unit is 128kg m-3. In certain units in which the unit of length is 25 cm and the unit of mass is 50g, the numerical value of density of the material is:

Physical quantity, n u =constant -

$n_{1}u_{1}=n_{2}u_{2}= constant$

$d=12.8\frac{kg}{M^{3}}=\frac{120\times 10^{3}g}{10^{6}cm^{3}}---------(1)$

now

50g equal to 1 unit of mass

so 1g equal to $\frac{1}{50}$ unit of mass

Similarly 25cm equal to 1 unit of length

so 1cm equal to $\frac{1}{25}$ unit of length

so

$1g\rightarrow \frac{1}{50\: \: }unit\: of\: \: mass\\\\1cm\rightarrow \frac{1}{25} unit\: of\: \: length$

so put in equation no.(1)

$d=\frac{128\times 10^{3}}{10^{6}}\frac{9}{cm^{3}}=\frac{128\times 10^{3}}{106}\times \frac{1}{50}\times \left ( \frac{1}{25} \right )^{3}=$

$=\frac{128\times (25)^{3}}{(10^{3})\times 50}\\\\\\\d=40 unit$

so ans is 40

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