Dimensional Consistency (equation Check)
Mediumphysics
Which equation is dimensionally consistent?
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Solution
Incorrect! Answer:
- Principle of Homogeneity: Every term in a physical equation must have the same dimensions.
- LHS Analysis: [s]=[L].
- RHS First Term: [ut]=[LT−1]×[T]=[L].
- RHS Second Term: [1/2at2]=[1]×[LT−2]×[T2]=[L].
- Verification: Since all terms match [L], the equation is dimensionally consistent.
- Counter-example check: F=mv⟹[MLT−2] on left, but [M][LT−1]=[MLT−1] on right (mismatch).
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About This Question
- Subject
- physics
- Chapter
- physics and measurement
- Topic
- dimensional consistency (equation check)
- Difficulty
- Medium
- Year
- 2025
Solution
- Principle of Homogeneity: Every term in a physical equation must have the same dimensions.
- LHS Analysis: [s]=[L].
- RHS First Term: [ut]=[LT−1]×[T]=[L].
- RHS Second Term: [1/2at2]=[1]×[LT−2]×[T2]=[L].
- Verification: Since all terms match [L], the equation is dimensionally consistent.
- Counter-example check: F=mv⟹[MLT−2] on left, but [M][LT−1]=[MLT−1] on right (mismatch).
This medium difficulty physics question is from the chapter physics and measurement, covering the topic of dimensional consistency (equation check). It appeared in the 2025 exam.
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