Units and conversion — express one newton (N) in dynes (CGS system).

Introduction / Context:
Engineering often requires converting between SI and CGS units. Force units include the newton (N) in SI and the dyne in CGS. Knowing the relationship enables quick dimensional checks and conversions in legacy literature and laboratory measurements.

Given Data / Assumptions:

• 1 N = 1 kg * m/s^2.
• 1 dyne = 1 g * cm/s^2.
• Conversion factors: 1 kg = 10^3 g; 1 m = 10^2 cm.

Concept / Approach:

Express the SI unit in CGS base units and collect powers of 10. This direct dimensional conversion avoids errors from intermediate approximations.

Step-by-Step Solution:

Verification / Alternative check:

Reverse check: 1 dyne = 10^-5 N, consistent with standard references.

Why Other Options Are Wrong:

10^3, 10^4, 10^6, and 10^7 dynes do not satisfy the base unit conversion factors.

Common Pitfalls:

Forgetting to convert both mass and length simultaneously; mixing MKS, SI, and CGS frameworks.

Final Answer:

10^5 dynes