Question

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

• A. $40\text{unit}$
• B. $4\text{unit}$
• C. $0.4\text{unit}$
• D. $0.04\text{unit}$

Answer 1

The correct option is A $40\text{units}$

In CGS system, $d=4{\text{g/cm}}^3$
Since, the unit of mass is $100\text{g}$ and unit of length is $10\text{cm}$,
Let us assume $1{\text{g}}^{{}^{\prime }}=100\text{g}$
$1{\text{cm}}^{{}^{\prime }}=10\text{cm}$

density, $d=\frac{4\left(\frac{1{\text{g}}^{{}^{\prime }}}{100}\right)}{{\left(\frac{1{\text{cm}}^{{}^{\prime }}}{10}\right)}^3}$
$\Rightarrow d=\frac{\left(\frac{4}{100}\right)\left(1{\text{g}}^{{}^{\prime }}\right)}{{\left(\frac{1}{10}\right)}^3(1{\text{cm}}^{{}^{\prime }}{)}^3}$
$\Rightarrow d=\frac{4\times {10}^3}{100}\text{unit}=40\text{units}$