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?
Select the correct option:
Solution
[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].
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
More dimensional analysis Practice Questions
A researcher derives the time period of a simple pendulum and suspects it depends on length and grav...
A researcher derives the time period of a simple pendulum and suspects it depends on length and grav...
A student tries to verify an equation containing a sum of a trigonometric term and a constant using ...
A student tries to verify an equation containing a sum of a trigonometric term and a constant using ...
A physicist examines the coefficient of viscosity that appears when describing the slow flow of hone...
A physicist examines the coefficient of viscosity that appears when describing the slow flow of hone...
While studying photon energy, a learner encounters Planck's constant in the relation linking energy ...
While studying photon energy, a learner encounters Planck's constant in the relation linking energy ...
A teacher writes the kinetic energy expression for a moving ball and asks students to confirm its di...
A teacher writes the kinetic energy expression for a moving ball and asks students to confirm its di...
An engineer notes that pressure and energy density appear in the same equation while studying a comp...
An engineer notes that pressure and energy density appear in the same equation while studying a comp...
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.
Looking for more practice? Explore all physics questions or browse physics and measurement questions on RankGuru.