A 13 m long iron rod weighs 23.4 kg. What is the weight of a 6 m length of the same rod (assume uniform density)?

Introduction / Context:
If a rod is uniform, its weight is directly proportional to its length. Therefore, a simple proportion can be used to find the weight of any other length of the same rod.

Given Data / Assumptions:

• 13 m length has weight 23.4 kg.
• Rod has uniform cross-section and density (weight ∝ length).
• Find weight for 6 m.

Concept / Approach:
Use the proportion Weight/Length = constant. Hence W2 = W1 * (L2/L1). This keeps units consistent and leverages direct proportionality.

Step-by-Step Solution:
W2 = 23.4 * (6 / 13)Compute numerator: 23.4 * 6 = 140.4Divide by 13: 140.4 / 13 = 10.8 kg

Verification / Alternative check:
Per-meter weight = 23.4 / 13 = 1.8 kg/m. For 6 m, weight = 1.8 * 6 = 10.8 kg, confirming the result.

Why Other Options Are Wrong:
7.2 kg or 9.6 kg correspond to other incorrect fractions; 12.4 kg and 18 kg exceed or mismatch the proportional outcome.

Common Pitfalls:
Using inverse proportion accidentally; rounding early and introducing errors; mixing meters and kilograms carelessly.

Final Answer:
10.8 kg