Density Unit Mistakes (g/cm³ vs kg/m³)
ρ = m/V is simple — until units disagree. These traps cost marks in density and buoyancy questions.
ρ = m / V — 1 g/cm³ = 1000 kg/m³ · 1 L = 0.001 m³
Trap 1: Mixing grams with cubic metres
Wrong: m = 250 g, V = 0.00025 m³ → ρ = 250 / 0.00025 without converting mass.
Right: Convert m = 0.250 kg first → ρ = 0.250 / 0.00025 = 1000 kg/m³.
Fix: Pair g with cm³ (→ g/cm³) or kg with m³ (→ kg/m³).
Trap 2: Treating liters as cubic metres
Wrong: V = 2 L into ρ = m/V with m in kg as if V were 2 m³.
Right: 2 L = 0.002 m³. Off-by-1000 errors are almost always liters vs m³.
Fix: 1 L = 0.001 m³ = 1000 cm³.
Trap 3: Forgetting 1 g/cm³ = 1000 kg/m³
Wrong: Aluminum 2.7 g/cm³ reported as 2.7 kg/m³ in an SI buoyancy formula.
Right: 2.7 g/cm³ = 2700 kg/m³.
Fix: Water is about 1 g/cm³ or 1000 kg/m³ — use that as a sanity check.
Trap 4: Putting object density into Fb = ρVg
Wrong: Using steel density for ρ when finding buoyant force in water.
Right: ρ in Fb = ρVg is the fluid density. Object density is for float/sink comparison.
Fix: Fresh water ≈ 1000 kg/m³ unless the problem gives salt water or another fluid.
Trap 5: Comparing density to weight
Wrong: “Density 800 kg/m³ is less than weight 20 N so it floats.”
Right: Compare densities (object vs fluid) or forces (W vs Fb) — never density to newtons.
Fix: Same kind of quantity on both sides of a comparison.
Bottom line
Match mass and volume units before dividing, convert g/cm³ ↔ kg/m³ with ×1000, and put fluid density — not object density — into Fb = ρVg.
FAQ
What is the density formula?
ρ = m / V. Rearrange to m = ρV or V = m/ρ with matching units.
How do I convert g/cm³ to kg/m³?
Multiply by 1000. Example: 2.7 g/cm³ → 2700 kg/m³.
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