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

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Q. The density of a material in $SI$ unit is $128\, kg\, m^{-3}$ . In certain units in which the unit of length is $25\, cm$ and the unit of mass is $50\, g$, the numerical value of density of the material is:

Physical World, Units and Measurements

Solution:

Density of material in $SI$ unit,
$= \frac{128 kg}{m^{3}}$
Density of material in new system
$= \frac{128\left(50g\right) \left(20\right)}{\left(25 cm\right)^{3} \left(4\right)^{3}}$
$ = \frac{128}{64} \times \left(20\right) = 40$ Unit