In the CGS system of units, 1 joule of energy is equal to how many ergs?

Introduction / Context:
Different unit systems are used in physics to measure the same physical quantities. In mechanics, the SI system uses joule as the unit of energy, while the older CGS system uses erg as the unit of energy. Converting between these units is a standard general knowledge point and is often tested in basic physics questions. This question asks how many ergs are contained in one joule.

Given Data / Assumptions:

• We know that SI base units for energy involve metre, kilogram and second.
• CGS base units for energy involve centimetre, gram and second.
• We want the numerical factor that converts 1 joule into ergs.
• We assume the standard conversion of metre to centimetre and kilogram to gram.

Concept / Approach:
In SI, one joule is defined as one newton metre. One newton is one kilogram metre per second squared. In CGS, one erg is defined as one dyne centimetre. One dyne is one gram centimetre per second squared. To convert between joules and ergs, we use the relations 1 kilogram equals 1000 grams and 1 metre equals 100 centimetres. Applying these conversions shows that one joule equals 10 raised to power 7 ergs.

Step-by-Step Solution:
Step 1: Write 1 joule as 1 newton metre, and 1 newton as 1 kilogram metre per second squared. Step 2: So 1 joule equals 1 kilogram metre squared per second squared. Step 3: Express kilogram in grams and metre in centimetres: 1 kilogram equals 10^3 grams and 1 metre equals 10^2 centimetres. Step 4: Therefore, 1 joule equals (10^3 grams) times (10^2 centimetres)^2 per second squared, which is 10^3 times 10^4 grams centimetre squared per second squared, giving 10^7 grams centimetre squared per second squared. Step 5: Since 1 erg is defined as 1 gram centimetre squared per second squared, it follows that 1 joule equals 10^7 ergs.

Verification / Alternative check:
You can remember this conversion using standard physics tables, which consistently list 1 joule equal to 10^7 ergs. The reverse conversion then becomes 1 erg equal to 10^-7 joules. This relation is widely used when comparing older CGS results with modern SI results in textbooks and exam problems. Checking multiple sources will always confirm the factor 10^7 as correct.

Why Other Options Are Wrong:
10^3 ergs, 10^4 ergs, 10^5 ergs and 10^6 ergs are too small by several orders of magnitude compared to the correct factor of 10^7.
If any of these smaller values were correct, the reverse conversion from ergs to joules would be inconsistent with known reference data and dimensional analysis.

Common Pitfalls:
Students often get confused by powers of ten, especially when dealing with multiple unit conversions at once. A frequent error is to write 1 joule equals 10^6 ergs or 10^5 ergs due to skipping one step in the squared metre to squared centimetre conversion. Always convert metre to centimetre first, then square the factor, and finally multiply by the kilogram to gram factor to avoid missing a power of ten.

Final Answer:
In the CGS system, 1 joule is equal to 10^7 ergs.