An amazing fact of Unobtanium (a new mineral discovered on the moon) is that it has a specific gravity of less than one. This means ____.

Question

BlackTom AI · Accepted Answer

Specific gravity (SG) is the ratio of a substance's density to the density of water at 4°C (by convention). Therefore SG < 1 means the mineral's density is less than that of water.

1) Relevant knowledge points
- Specific gravity: SG = ρ_substance / ρ_water.
- Density of water ≈ 1.00 g·cm⁻³ (or 1000 kg·m⁻³).
- Archimedes' principle: buoyant force on an immersed body equals the weight of the displaced fluid. An object floats when its weight is balanced by the buoyant force (or its average density is less than the fluid).

2) Step-by-step reasoning
- From SG definition: SG < 1 ⇒ ρ_unobtanium < ρ_water.
- Let the mineral have volume V and density ρ_u. Its weight = ρ_u · V · g.
- If partially submerged with V_disp displaced, buoyant force = ρ_water · V_disp · g.
- For equilibrium (floating): ρ_u · V · g = ρ_water · V_disp · g ⇒ V_disp / V = ρ_u / ρ_water = SG.
- Since SG < 1, V_disp / V < 1, so only part of the mineral needs to be submerged to displace enough water to support its weight — it floats.

3) Numerical illustration
- Suppose SG = 0.8 so ρ_u = 0.8 g·cm⁻³. For V = 1 cm³: weight = 0.8 g (times g). Displacing 1 cm³ of water provides buoyant support equal to 1.0 g (times g), which exceeds the mineral's weight; equilibrium occurs when 0.8 cm³ is submerged (80% submerged), so it floats.

4) Why the correct answer is correct
- Because SG < 1 directly implies the mineral's density is lower than water, so the buoyant force from displacing a fraction of the mineral’s volume of water equals its weight. That condition is the definition of floating.

5) Why other interpretations would be incorrect
- Misreading SG < 1 as “lighter than water” without specifying density is ambiguous; floating depends on density, not mass. SG < 1 does not mean it dissolves or is gaseous. It simply means less dense than water and therefore buoyant.

6) Conclusion
- The correct conclusion is that unobtanium will float on water, which matches the provided answer: it will float on water.

An amazing fact of Unobtanium (a new mineral discovered on the moon) is that it has a specific gravity of less than one. This means ____.Single choice

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