Dimensional Analysis (checking Formula)
Hardphysics
For a formula for speed v = A t + B/t, dimensions of A and B must be respectively?
Select the correct option:
Solution
Incorrect! Answer:
- Homogeneity: The dimensions of v must match the dimensions of each term on the right (At and B/t).
- Speed dimension: [v]=[LT−1].
- Solve for A:
- [At]=[LT−1]
- [A][T]=[LT−1]⟹[A]=[LT−2] (Acceleration dimensions).
- Solve for B:
- [B/t]=[LT−1]
- [B][T−1]=[LT−1]⟹[B]=[L] (Length dimensions).
- Conclusion: A has dimensions of LT−2 and B has dimensions of L.
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About This Question
- Subject
- physics
- Chapter
- physics and measurement
- Topic
- dimensional analysis (checking formula)
- Difficulty
- Hard
- Year
- 2025
Solution
- Homogeneity: The dimensions of v must match the dimensions of each term on the right (At and B/t).
- Speed dimension: [v]=[LT−1].
- Solve for A:
- [At]=[LT−1]
- [A][T]=[LT−1]⟹[A]=[LT−2] (Acceleration dimensions).
- Solve for B:
- [B/t]=[LT−1]
- [B][T−1]=[LT−1]⟹[B]=[L] (Length dimensions).
- Conclusion: A has dimensions of LT−2 and B has dimensions of L.
This hard difficulty physics question is from the chapter physics and measurement, covering the topic of dimensional analysis (checking formula). It appeared in the 2025 exam.
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