Question

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

• A. $0.4$
• B. $0.04$
• C. $40$
• D. $400$

Answer 1

The correct option is C $40$

Given-
$\rho =4{\text{g/cm}}^3,\text{Unit of length}=10\text{cm},\text{Unit of mass}=100\text{g}$

From the given data,
$10\text{cm}\text{gives one unit of length}$
So,
$1\text{cm}=\frac{1}{10}\text{unit}$
Likewise,
$1\text{g}=\frac{1}{100}\text{unit}$
In CGS
$\rho =4\frac{\text{g}}{{\text{cm}}^3}$
$\rho =\frac{4\left(\frac{1}{100}\right)}{{\left(\frac{1}{10}\right)}^3}$
$\rho =\frac{4\times (10{)}^3}{100}=40\text{Units}$