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Specific weight (weight per unit volume): select the correct S.I. unit used in mechanics and fluid statics.

Difficulty: Easy

Correct Answer: N/m3

Explanation:


Introduction / Context:
Specific weight (often denoted gamma) equals weight per unit volume and is distinct from density. In hydrostatics, gamma appears in equations for pressure variation with depth and buoyancy calculations. Correct unit identification helps avoid mixing mass-based and weight-based properties.


Given Data / Assumptions:

  • Weight W = m * g (units N).
  • Volume V has unit m^3.
  • Specific weight gamma = W / V.


Concept / Approach:
Because weight is a force, the numerator carries the unit newton (N). Dividing by volume m^3 yields N/m^3. This distinguishes gamma from density (kg/m^3) and from pressure (N/m^2).


Step-by-Step Solution:

Write definition: gamma = W / V.Insert S.I. units: W → N; V → m^3; therefore gamma unit = N/m^3.Relate to density: gamma = rho * g → units: (kg/m^3) * (m/s^2) = kg·m/(m^3·s^2) = N/m^3 (since 1 N = 1 kg·m/s^2).


Verification / Alternative check:

For water near 4°C: rho ≈ 1000 kg/m^3; gamma ≈ 1000 * 9.81 ≈ 9810 N/m^3 (≈ 9.81 kN/m^3).


Why Other Options Are Wrong:

kg/m3: density, not specific weight.N/m2: pressure (pascal), not specific weight.none of these / kg·m/s3: do not match the definition.


Common Pitfalls:

Treating density and specific weight as interchangeable; they differ by factor g.Confusing pressure with specific weight due to similar-looking unit forms.


Final Answer:

N/m3
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