The density of a material in CGS system of units is $$4g/c{m^3}.$$ 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
A.
$$0.4$$
B.
$$40$$
C.
$$400$$
D.
$$0.04$$
Answer :
$$40$$
Solution :
In CGS system, $$d = 4\frac{g}{{c{m^3}}}$$
The unit of mass is $$100\,g$$ and unit of length is $$10\,cm,$$ so
$$\eqalign{
& {\text{density}} = \frac{{4\left( {\frac{{100g}}{{100}}} \right)}}{{{{\left( {\frac{{10}}{{10}}cm} \right)}^3}}} = \frac{{\left( {\frac{4}{{100}}} \right)}}{{{{\left( {\frac{1}{{10}}} \right)}^3}}}\frac{{\left( {100g} \right)}}{{{{\left( {10\,cm} \right)}^3}}} \cr
& = \frac{4}{{100}} \times {\left( {10} \right)^3} \cdot \frac{{100g}}{{{{\left( {10\,cm} \right)}^3}}} = 40\,unit \cr} $$
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