`rho=2g//cm^(3)` convert it into MKS system -

Options

A. `2xx10^(-3)(kg)/(m^(3))`
B. `2xx10^(3)(kg)/(m^(3))`
C. `4xx10^(3)(kg)/(m^(3))`
D. `2xx10^(6)(kg)/(m^(3))`

Answer

To convert the density \( \rho = 2 \, \text{g/cm}^3 \) into the MKS system (Kilograms per cubic meter), we will follow these steps:

### Step 1: Convert grams to kilograms
We know that:
\[ 1 \, \text{kg} = 1000 \, \text{g} \]
Thus, to convert grams to kilograms, we can express grams in terms of kilograms:
\[ 2 \, \text{g} = \frac{2}{1000} \, \text{kg} = 0.002 \, \text{kg} \]

### Step 2: Convert cubic centimeters to cubic meters
Next, we need to convert cubic centimeters to cubic meters. We know that:
\[ 1 \, \text{m} = 100 \, \text{cm} \]
Therefore,
\[ 1 \, \text{cm} = \frac{1}{100} \, \text{m} \]
To convert cubic centimeters to cubic meters, we cube both sides:
\[ 1 \, \text{cm}^3 = \left(\frac{1}{100} \, \text{m}\right)^3 = \frac{1}{1000000} \, \text{m}^3 = 10^{-6} \, \text{m}^3 \]

### Step 3: Substitute the conversions into the density formula
Now we can substitute the conversions into the density formula:
\[ \rho = \frac{2 \, \text{g}}{\text{cm}^3} = \frac{0.002 \, \text{kg}}{10^{-6} \, \text{m}^3} \]

### Step 4: Simplify the expression
Now we simplify the expression:
\[ \rho = \frac{0.002}{10^{-6}} \, \text{kg/m}^3 = 0.002 \times 10^{6} \, \text{kg/m}^3 = 2000 \, \text{kg/m}^3 \]

### Final Answer
Thus, the density in the MKS system is:
\[ \rho = 2000 \, \text{kg/m}^3 \]

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