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