Subjects · Leaving Cert Applied Maths
Leaving Cert Applied Maths: Dimensional analysis
How often Dimensional analysis comes up on the Applied Maths papers, every year it was asked, and questions to try.
HL Asked on 2 of the last 3 Higher Level papers, most recently in 2024. most years
OL Asked on 2 of the last 3 Ordinary Level papers, most recently in 2024. most years
Quick ones on Dimensional analysis.
- kg m s⁻¹
- kg m s⁻²
- kg m² s⁻²
- kg m² s⁻¹
- kg m s⁻²
- kg m s⁻¹
- kg m² s⁻²
- kg m² s⁻¹
- kg m s⁻²
Show the answers
(a) kg m s⁻²
(b) kg m s⁻¹
(c) kg m² s⁻²
Higher Level
Asked on 2 of the last 3 Higher Level papers, most recently in 2024. most years
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2025 | Not asked |
| 2024 | Q8 |
| 2023 | Q3 |
Links open the State Examinations Commission’s paper for that year.
More Dimensional analysis questions
Dimensional analysis, 3 marks
Units of k in the drag law F = kv², in base SI units?
- kg s⁻¹
- kg m s⁻¹
- kg m⁻¹
Show the answer
kg m⁻¹
k = F ÷ v² = (kg m s⁻²) ÷ (m² s⁻²) = kg m⁻¹. For F = kv the units would instead be kg s⁻¹, so the units of k depend on the drag law.
Dimensional analysis, 3 marks
Why is the formula v = u + at² dimensionally wrong?
- t is dimensionless in this formula
- at² has units of m, not m s⁻¹
- a has no units, so at² is s²
Show the answer
at² has units of m, not m s⁻¹
Every term added must have the same units. v and u are m s⁻¹, but at² is m s⁻² × s² = m. So the formula cannot be right, whatever the constant.
Dimensional analysis, 3 marks
The centripetal force mv²/r in base SI units?
- kg m s⁻²
- kg m² s⁻²
- kg s⁻²
Show the answer
kg m s⁻²
kg × (m s⁻¹)² ÷ m = kg m² s⁻² ÷ m = kg m s⁻², which is the newton, as a force must be. Forgetting to divide by r gives the units of energy.
Ordinary Level
Asked on 2 of the last 3 Ordinary Level papers, most recently in 2024. most years
Every paper, year by year
| Year | Where it came up |
|---|---|
| 2025 | Not asked |
| 2024 | Q2 |
| 2023 | Q5 |
Links open the State Examinations Commission’s paper for that year.
More Dimensional analysis questions
Dimensional analysis, 3 marks
What are the dimensions of kinetic energy?
- kg m s⁻²
- kg m² s⁻¹
- kg m² s⁻²
Show the answer
kg m² s⁻²
KE = ½mv². The ½ has no dimensions, so kg × (m s⁻¹)² = kg m² s⁻². This is one joule.
Dimensional analysis, 2 marks
What are the dimensions of angular velocity ω?
- m s⁻²
- s⁻¹
- m s⁻¹
Show the answer
s⁻¹
Radians are a ratio of two lengths, so they have no dimensions. ω in rad s⁻¹ has dimensions s⁻¹.
Dimensional analysis, 2 marks
What are the dimensions of force?
- kg m s⁻²
- kg m s⁻¹
- kg m² s⁻²
Show the answer
kg m s⁻²
F = ma, so force has dimensions kg × m s⁻² = kg m s⁻². This is one newton.
Other Applied Maths topics
- Calculus & variable acceleration
- Connected particles & pulleys
- Constant acceleration (suvat)
- Dijkstra's algorithm
- Displacement & velocity graphs
- First-order difference equations
- Forces & Newton's laws
- Friction & inclined planes
- Graphs & network terminology
- Horizontal circular motion
- Loans, savings & finance models
- Matrices & adjacency
- Minimum spanning trees
- Momentum & direct collisions
- Oblique collisions
- Projectile motion
- Recurrence relations & differences
- Reducing second-order DEs
- Resisted motion & drag
- Second-order difference equations
- Separable differential equations
- The modelling cycle & assumptions
- Vectors & the dot product
- Vertical circular motion
- Dynamic programming & Bellman
- Project scheduling & critical path
- Work, energy & conservation
- Greedy vs dynamic algorithms
- Hooke's law & elastic energy