1dyne is equal to

Options

A. 980 g wt
B. `1/980` g wt
C. 980 kg wt
D. None of these

Explanation

To solve the question "1 dyne is equal to", we need to understand the relationship between dyne, newton, and gram weight. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding Dyne**:
- Dyne is a unit of force in the CGS (centimeter-gram-second) system.

2. **Conversion from Dyne to Newton**:
- We know that 1 dyne is equal to \(10^{-5}\) newtons.
\[ 1 \text{ dyne} = 10^{-5} \text{ N} \]

3. **Understanding Newton**:
- 1 newton is defined as the force required to accelerate a mass of 1 kg at a rate of 1 m/s².
- In terms of weight, 1 newton can also be expressed in terms of grams. Since \(1 \text{ N} \approx 9.80 \text{ kg}\), we can express it as:
\[ 1 \text{ N} = \frac{1}{9.80} \text{ kg} \]

4. **Substituting Newton in Dyne**:
- Now, substituting the value of 1 N into the dyne equation:
\[ 1 \text{ dyne} = 10^{-5} \times \frac{1}{9.80} \text{ kg} \]

5. **Converting Kilograms to Grams**:
- Since 1 kg = 1000 grams, we can convert the equation:
\[ 1 \text{ dyne} = 10^{-5} \times \frac{1}{9.80} \times 1000 \text{ g} \]

6. **Simplifying the Expression**:
- This simplifies to:
\[ 1 \text{ dyne} = \frac{10^{-5} \times 1000}{9.80} \text{ g} = \frac{10^{-2}}{9.80} \text{ g} \]

7. **Final Result**:
- Thus, we find that:
\[ 1 \text{ dyne} = \frac{1}{9.80} \text{ g weight} \]

### Conclusion:
The correct answer is option 2: \(1 \text{ dyne} = \frac{1}{9.80} \text{ g weight}\).

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