The ratio of SI to cgs units of force is

Options

A. `10 ^(-5)`
B. `10^5`
C. `10 ^(-3)`
D. `10^3`

Explanation

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

### Step 1: Understand the units of force in both systems
- The SI unit of force is the Newton (N), which is defined as:
\[ 1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2 \]
- The CGS unit of force is the Dyne (dyn), which is defined as:
\[ 1 \text{ dyn} = 1 \text{ g} \cdot \text{cm/s}^2 \]

### Step 2: Write down the relationship between the units
- We need to express the SI unit in terms of CGS units. Therefore, we will convert kilograms to grams and meters to centimeters:
- \(1 \text{ kg} = 1000 \text{ g}\)
- \(1 \text{ m} = 100 \text{ cm}\)

### Step 3: Substitute the conversions into the SI unit of force
- Now we can express the Newton in terms of dynes:
\[ 1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2 = (1000 \text{ g}) \cdot (100 \text{ cm}) / \text{s}^2 \]
- This simplifies to:
\[ 1 \text{ N} = 100000 \text{ g} \cdot \text{cm/s}^2 = 10^5 \text{ dyn} \]

### Step 4: Calculate the ratio of SI to CGS units
- Now, we can find the ratio of SI unit (Newton) to CGS unit (Dyne):
\[ \text{Ratio} = \frac{1 \text{ N}}{1 \text{ dyn}} = \frac{10^5 \text{ dyn}}{1 \text{ dyn}} = 10^5 \]

### Conclusion
- The ratio of SI to CGS units of force is:
\[ \text{Ratio} = 10^5 \]

### Final Answer
- The correct answer is option 2: \(10^5\).

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