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The density of material in CGS system of units is 4g/cm3. In a system of units in which unit of length is 10 cm and unit of mass is 100g, the value of density of material will be

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@Sushant

Density in CGS system is =  4  gms/ cm³ 

Another system of units:
       unit of mass =  gm' = 100 gm             unit of length = cm' = 10 cm

1 gm = \frac{gm'}{100}        and    1 cm = \frac{cm'}{10}

Substitute these values in the value of the density.  Now density of the material:

= 4 \frac{gm}{cm^3}\\\\= 4\ (\frac{gm'}{100})\ \frac{1}{(\frac{cm'}{10})^3}\\\\=4 \frac{1}{100}\ gm'\ \frac{10^3}{cm'^3}\\\\=\frac{4*10^3}{100}\ \frac{gm'}{cm'^3}\\\\=40\frac{gm'}{cm'^3}

Thus in the new system the value of density will be 40 units.

 

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avinash.dongre

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