BASICS OF UNITS — Select the correct conversion. Question: One joule equals how many ergs?

Introduction / Context:
Joule (J) is the SI unit of energy, while the cgs unit is the erg. Converting between SI and cgs systems is a staple skill in physics and engineering fundamentals.

Given Data / Assumptions:

• 1 J = 1 Nm and 1 N = 10^5 dynes; 1 m = 10^2 cm.
• 1 erg = 1 dynecm.
• We seek a pure numerical factor relating J and erg.

Concept / Approach:
Use base conversions systematically. Express the SI unit (Nm) in cgs (dynecm) and match to the definition of the erg. Careful tracking of powers of ten yields the final factor.

Step-by-Step Solution:
Start: 1 J = 1 Nm.Convert force: 1 N = 10^5 dynes.Convert length: 1 m = 10^2 cm.Therefore: 1 J = (10^5 dynes) * (10^2 cm) = 10^7 dynecm = 10^7 ergs.

Verification / Alternative check:
Reverse: 1 erg = 10^-7 J. This reciprocal relation consistently appears in reference tables and problem solutions.

Why Other Options Are Wrong:
A) 10^5 ergs — underestimates by 100x.B) 10^3 ergs — off by a factor of 10,000.D) 10^11 ergs — overestimates by 10,000.E) 10^9 ergs — incorrect scaling.

Common Pitfalls:
Losing track of powers when converting both force and length. Do them stepwise and multiply exponents: 10^5 * 10^2 = 10^7.

Final Answer:
10^7 ergs