A metal rod of density 7000 kgm-3 and cross-sectional area of 0.001257m2 has a mass of 1.76kg. Calculate its length.

Analyze the question: We are given density, cross-sectional area and mass of a rod, and we need its length.

Concept: Density = mass / volume, and the volume of a uniform rod = cross-sectional area × length.

So:

• Volume V = m / ρ
• Length L = V / A = m / (ρA)

Solution:

1. Volume: V = 1.76 / 7000 = 2.514 × 10⁻⁴ m³

2. Length: L = V / A = (2.514 × 10⁻⁴) / (0.001257) L = 0.2000 m

Check: 7000 × 0.001257 = 8.799, and 1.76 / 8.799 ≈ 0.2000 m.

Answer: The length is 0.20 m, which is option A.

Tip: For rod, wire or cylinder problems, combine the formulas into one: L = m / (ρA). Also, quickly estimate: 7000 × 0.00126 ≈ 8.8, and 1.76 is exactly one-fifth of 8.8, so L = 0.2 m. Spotting these neat ratios saves time in the exam.