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  4. The density of a material in SI units 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 units 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 :

JEE MainJEE Main 2019Physical World, Units and Measurements

Solution:

$\frac{128 kg}{m^{3}} = \frac{125 \left(50g\right)\left(20\right)}{\left(25cm\right)^{3}\left(4\right)^{3}} $
$ = \frac{128}{64} \left(20\right)units $
$ = 40\, units $