📐 Use of Fundamental Units in Physical Equations to Examine Their Homogeneity

Homogeneity of an Equation means that both sides of a physical equation have the same unit. This helps verify the equation is physically meaningful.

Example 1: s = ut + ½at²

Let’s check units:

  • s (displacement) → metre (m)

  • u (initial velocity) → m/s

  • t (time) → s

  • a (acceleration) → m/s²

  • t² → s²

LHS: s = m
RHS:

  • ut = (m/s) × s = m

  • ½at² = (m/s²) × s² = m

✅ Both sides have unit metre (m) ⇒ Equation is homogeneous.

Conclusion:

  • Checking for unit homogeneity ensures that equations are valid and logically correct in physics.

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