Dimensional Analysis
In the equation x = a t^2 + b t + c describing the displacement of a particle with time, what are the respective dimensions of constants a, b and c?
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Which combination has dimensions of pressure?
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About This Question
- Subject
- physics
- Chapter
- physics and measurement
- Topic
- dimensional analysis
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
[LT−2],[LT−1],[L]
The principle of dimensional homogeneity requires every additive term in a physically valid equation to carry the same dimensions, here those of displacement x, namely length [L]. Examining the first term a t^2: since t^2 has dimensions [T^2], the constant a must supply [L]/[T^2] = [L T^-2] so that the product becomes [L]; this is exactly the dimension of acceleration. For the middle term b t, the factor t contributes [T], so b must have dimensions [L]/[T] = [L T^-1], the dimension of velocity. The last term c stands alone and must itself carry the dimension of displacement, [L]. The option [L], [L T^-1], [L T^-2] reverses the roles of a and c and is therefore wrong. The option [L T^-2], [L], [L T^-1] misassigns b and c. The option [L T^-1], [L T^-2], [L] swaps the dimensions of a and b. This mirrors the kinematic equation x = ut + (1/2)at^2 from NCERT. A consistency check confirms each term reduces cleanly to [L].
This medium difficulty physics question is from the chapter physics and measurement, covering the topic of dimensional analysis. It appeared in the 2025 exam.
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