π 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 + Β½atΒ²
Letβs check units:
s (displacement) β metre (m)
u (initial velocity) β m/s
t (time) β s
a (acceleration) β m/sΒ²
tΒ² β sΒ²
LHS: s = m
RHS:
ut = (m/s) Γ s = m
Β½atΒ² = (m/sΒ²) Γ sΒ² = m
β Both sides have unit metre (m) β Equation is homogeneous.
Conclusion:
Checking for unit homogeneity ensures that equations are valid and logically correct in physics.
