The density of mercury is 13.6 g `cm^(-3)` in CGS system. Find its value in SI units.

Answer

To convert the density of mercury from CGS units to SI units, follow these steps:

1. **Identify the given density in CGS units:**
\[ \rho_{\text{CGS}} = 13.6 \, \text{g/cm}^3 \]

2. **Convert grams to kilograms:**
\[ 1 \, \text{g} = 10^{-3} \, \text{kg} \]
Therefore,
\[ 13.6 \, \text{g} = 13.6 \times 10^{-3} \, \text{kg} \]

3. **Convert cubic centimeters to cubic meters:**
\[ 1 \, \text{cm} = 10^{-2} \, \text{m} \]
Therefore,
\[ 1 \, \text{cm}^3 = (10^{-2} \, \text{m})^3 = 10^{-6} \, \text{m}^3 \]

4. **Combine the conversions to find the density in SI units:**
\[ \rho_{\text{SI}} = \frac{13.6 \times 10^{-3} \, \text{kg}}{10^{-6} \, \text{m}^3} \]

5. **Simplify the expression:**
\[ \rho_{\text{SI}} = 13.6 \times 10^{-3} \times 10^{6} \, \text{kg/m}^3 \]
\[ \rho_{\text{SI}} = 13.6 \times 10^{3} \, \text{kg/m}^3 \]

6. **Final answer:**
\[ \rho_{\text{SI}} = 13.6 \times 10^{3} \, \text{kg/m}^3 \]

So, the density of mercury in SI units is \( 13.6 \times 10^3 \, \text{kg/m}^3 \).