Number System — A 13 m long rod weighs 23.4 kg. Assuming uniform density, find the weight of a 6 m length of the same rod.

Introduction / Context:
Linear scaling applies to uniform rods: weight is proportional to length when cross-section and material are constant. Therefore, finding the weight of another length simply requires a ratio or unit rate approach.

Given Data / Assumptions:

• Weight of 13 m rod = 23.4 kg.
• Uniform cross-section and material (constant mass per meter).
• Find weight for 6 m of the same rod.

Concept / Approach:
Compute mass per meter first, then multiply by the target length. This method avoids proportionality mistakes and keeps numbers small and manageable.

Step-by-Step Solution:
1) Mass per meter = 23.4 kg / 13 m = 1.8 kg/m.2) Weight for 6 m = 1.8 kg/m * 6 m = 10.8 kg.3) Therefore, the 6 m length weighs 10.8 kg.

Verification / Alternative check:
Proportion method: 23.4 : 13 = x : 6 → x = 23.4 * 6 / 13 = 140.4 / 13 = 10.8 kg. Matches the unit-rate method.

Why Other Options Are Wrong:
7.2 kg and 9.6 kg undercount by using 1.2 or 1.6 kg/m; 12.4 kg and 18.0 kg overcount; only 10.8 kg matches the uniform-density assumption.

Common Pitfalls:
Rounding mass per meter too early; mixing meters and centimeters; forgetting proportional scaling.

Final Answer:
10.8 kg