Mass density from mass and volume: The mass of 2.5 m^3 of a certain liquid is 2 tonnes. Determine the mass density (kg/m^3).

Introduction / Context:Mass density (often simply “density”) is mass per unit volume. Many property calculations in fluid mechanics begin with this basic relationship to connect mass, volume, and weight. This problem is a straightforward unit-consistency and division exercise.

Given Data / Assumptions:

• Mass m = 2 tonnes = 2000 kg (1 tonne = 1000 kg).
• Volume V = 2.5 m^3.
• Uniform material (single liquid with uniform density).

Concept / Approach:Use the definition ρ = m / V. Ensure both mass and volume are in SI units (kg and m^3). The result directly yields kg/m^3.

Step-by-Step Solution:

Verification / Alternative check:Cross-check using weight density if needed: γ = ρ * g ≈ 800 * 9.81 ≈ 7.85 kN/m^3 (for context), aligning with a light hydrocarbon-like liquid rather than water.

Why Other Options Are Wrong:

• 200 / 400 / 600 kg/m^3: Each would require either a smaller mass or a larger volume than given; they do not satisfy m = 2000 kg and V = 2.5 m^3.

Common Pitfalls:Forgetting tonne-to-kg conversion; inverting the ratio (V/m instead of m/V); mixing weight (N) with mass (kg).

Final Answer:800 kg/m^3