Direct proportion for uniform material: If 45 m of a uniform rod weighs 171 kg, what will be the weight (in kilograms) of 12 m of the same rod, assuming the rod has constant density and cross-section throughout its length?

Introduction / Context:
Uniform rods have constant mass per unit length. Therefore, the weight is directly proportional to length. This unitary-method problem scales a known length–weight pair to a new length using constant density.

Given Data / Assumptions:

• Length L1 = 45 m
• Weight W1 = 171 kg
• Required length L2 = 12 m
• Rod is uniform (same mass per meter).

Concept / Approach:
Mass per meter = W1 / L1. Weight for any length L is (mass per meter) * L. This is a simple direct proportion: W ∝ L for uniform materials.

Step-by-Step Solution:
Mass per meter = 171 / 45 = 3.8 kg/mWeight for 12 m = 3.8 * 12 = 45.6 kg

Verification / Alternative check:
Set up a ratio: W2 / W1 = L2 / L1 → W2 = 171 * (12 / 45) = 171 * 0.2666… = 45.6 kg. Same result confirms correctness.

Why Other Options Are Wrong:
49 kg and 55 kg assume higher mass per meter; 42.5 kg and 40.8 kg assume lower mass per meter, contradicting the given 45 m to 171 kg relation.

Common Pitfalls:
Rounding too early when computing mass per meter. Keep decimals exact until the final multiplication to avoid compounding errors.

Final Answer:
45.6 kg