The correct relation between joule and erg is

Options

A. `1 J = 10^(-5)` erg
B. `1 J = 10^(5)` erg
C. `1 J = 10^(-7)` erg
D. `1 J = 10^(7)` erg

Explanation

To find the correct relation between Joule and Erg, we can follow these steps:

### Step 1: Understand the Units
1 Joule (J) is the SI unit of energy, while 1 Erg (erg) is the CGS (centimeter-gram-second) unit of energy.

### Step 2: Convert Joules to Ergs
We start with the definition of 1 Joule:
\[ 1 \text{ Joule} = 1 \text{ kg} \cdot \text{m}^2/\text{s}^2 \]

### Step 3: Convert Kilograms to Grams
We know that:
\[ 1 \text{ kg} = 1000 \text{ g} = 10^3 \text{ g} \]

### Step 4: Convert Meters to Centimeters
We also know that:
\[ 1 \text{ m} = 100 \text{ cm} = 10^2 \text{ cm} \]

### Step 5: Substitute the Conversions
Now, substituting these conversions into the Joule equation:
\[ 1 \text{ Joule} = (10^3 \text{ g}) \cdot (10^2 \text{ cm})^2/\text{s}^2 \]
This simplifies to:
\[ 1 \text{ Joule} = (10^3 \text{ g}) \cdot (10^4 \text{ cm}^2)/\text{s}^2 \]

### Step 6: Combine the Terms
Combining the terms gives:
\[ 1 \text{ Joule} = 10^7 \text{ g} \cdot \text{cm}^2/\text{s}^2 \]

### Step 7: Relate to Ergs
Since 1 Erg is defined as:
\[ 1 \text{ erg} = 1 \text{ g} \cdot \text{cm}^2/\text{s}^2 \]
We can now express Joules in terms of Ergs:
\[ 1 \text{ Joule} = 10^7 \text{ erg} \]

### Conclusion
Thus, the correct relation between Joule and Erg is:
\[ 1 \text{ Joule} = 10^7 \text{ erg} \]

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