dimensional consistency (equation check)

Question

Which equation is dimensionally consistent?

RankGuru · Accepted Answer

1. **Principle of Homogeneity**: Every term in a physical equation must have the same dimensions.
2. **LHS Analysis**: $[s] = [L]$.
3. **RHS First Term**: $[ut] = [LT^{-1}] 	imes [T] = [L]$.
4. **RHS Second Term**: $[1/2 a t^2] = [1] 	imes [LT^{-2}] 	imes [T^2] = [L]$.
5. **Verification**: Since all terms match $[L]$, the equation is **dimensionally consistent**.
6. **Counter-example check**: $F=mv \implies [MLT^{-2}]$ on left, but $[M][LT^{-1}] = [MLT^{-1}]$ on right (mismatch).

Rank Guru

dimensional consistency (equation check)

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