Using dimensional analysis obtain the value of density of water in S.I. In C.G.S system density of water is `1gm//cm^(3)`.

Explanation

To find the density of water in the SI system using dimensional analysis, we start with the known density of water in the CGS system.

### Step-by-Step Solution:

1. **Understanding Density**:
Density (ρ) is defined as mass (m) per unit volume (V). The formula for density is:
\[ \rho = \frac{m}{V} \]

2. **Known Value in CGS**:
In the CGS system, the density of water is given as:
\[ \rho_{CGS} = 1 \, \text{g/cm}^3 \]

3. **Converting Units**:
We need to convert the CGS units to SI units.
- 1 gram (g) = \(10^{-3}\) kilograms (kg)
- 1 centimeter (cm) = \(10^{-2}\) meters (m)

4. **Expressing Density in SI Units**:
Now, we can express the density in SI units:
\[ \rho_{SI} = \frac{1 \, \text{g}}{1 \, \text{cm}^3} \]
Substituting the conversions:
\[ \rho_{SI} = \frac{1 \times 10^{-3} \, \text{kg}}{(1 \times 10^{-2} \, \text{m})^3} \]

5. **Calculating Volume in SI Units**:
The volume in SI units becomes:
\[ (1 \times 10^{-2} \, \text{m})^3 = 1 \times 10^{-6} \, \text{m}^3 \]

6. **Final Calculation of Density**:
Now substituting back into the density formula:
\[ \rho_{SI} = \frac{1 \times 10^{-3} \, \text{kg}}{1 \times 10^{-6} \, \text{m}^3} = 1000 \, \text{kg/m}^3 \]

7. **Conclusion**:
Therefore, the density of water in the SI system is:
\[ \rho_{SI} = 1000 \, \text{kg/m}^3 \]