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The density of a material in $CGS$ system of units is $4 g / {cm}^{3}$ . In a system of units in which unit of length is $10 cm$ and unit of mass is $100 g$ , the value of density of material will be:

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answer is 40.

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Detailed Solution

Density of material,

$d_{1} = n_{1} u_{1} = 4 {gcm}^{- 3}$

$n_{1} u_{1} = n_{2} u_{2} \Rightarrow n_{2} = n_{1} (\frac{u_{1}}{u_{2}})$

$\Rightarrow n_{2} = 4 (\frac{1 g}{100 g}) [\frac{1 {cm}^{- 3}}{{(10 cm)}^{- 3}}] = 40$

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