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 units of mass is $50 g$ , the numerical value of density of the material is _______.

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answer is 40.

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Detailed Solution

For the two system of units,

$N_{1} u_{1} = N_{2} u_{2} \Rightarrow \frac{128 kg}{m^{3}} = N_{2} \times \frac{50 g}{(25^{3} {cm}^{3})} \Rightarrow N_{2} = \frac{128 \times 10^{3}}{10^{6}} \times \frac{{(25)}^{3}}{50} = 40$

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