The ratio of Si to cgs units of buoyant force Is

Options

A. `10^3`
B. `10^4`
C. `10^5`
D. `10^6`

Explanation

To find the ratio of the SI to CGS units of buoyant force, we will follow these steps:

### Step 1: Understand the Units of Buoyant Force
Buoyant force is a type of force, and its unit in the SI system is the Newton (N). The CGS unit for force is the dyne.

### Step 2: Identify the Units
- **SI Unit of Force (Buoyant Force)**:
- 1 Newton (N) = 1 kg·m/s²
- **CGS Unit of Force (Buoyant Force)**:
- 1 dyne = 1 g·cm/s²

### Step 3: Convert SI Units to CGS Units
To find the ratio, we need to express the SI unit in terms of CGS units:
1. Convert kilograms to grams:
- 1 kg = 1000 g
2. Convert meters to centimeters:
- 1 m = 100 cm

### Step 4: Substitute Units
Now, substituting these conversions into the SI unit:
- 1 N = 1 kg·m/s²
- 1 N = (1000 g)·(100 cm)/s²
- 1 N = 100000 g·cm/s²

### Step 5: Calculate the Ratio
Now we can find the ratio of SI to CGS units:
- 1 N = 100000 dyne
- Therefore, the ratio of SI unit (Newton) to CGS unit (dyne) is:
\[ \text{Ratio} = \frac{1 \text{ N}}{1 \text{ dyne}} = \frac{100000 \text{ dyne}}{1 \text{ dyne}} = 10^5 \]

### Conclusion
The ratio of SI to CGS units of buoyant force is \(10^5\).

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