A detailed physics-themed digital illustration featuring rulers, vectors, electromagnetic fields, waves, formulas, dimensional symbols, and measurement tools — without any written text.
Introduction: Why Dimensional Analysis Matters for CUET, NEET & JEE Aspirants
Dimensional Analysis is one of the most scoring and conceptually rich chapters in NCERT Class 11 Units & Measurements. Whether you are preparing for CUET Physics, the NEET UG exam, or JEE Main/Advanced, understanding dimensions, units, and the mathematical relationships between physical quantities is absolutely essential.
This chapter offers high-yield marks because:
- Questions are direct and formula-based
- No heavy calculation is required
- Units, dimensions & derived quantities appear across all physics chapters
- CUET specifically asks multi-concept MCQs with dimensional reasoning
This blog includes:
- Comprehensive conceptual explanations
-
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NEET physics units and dimensional analysis numericals, etc. - A massive MCQ Practice Section with answers included immediately after each question
Let’s begin mastering one of the most foundational topics of physics.
Understanding Dimensions: A Quick Refresher
Every physical quantity—whether force, pressure, energy, power, or angular momentum—can be represented in terms of the fundamental dimensions:
- Mass (M)
- Length (L)
- Time (T)
- Electric Current (A)
- Temperature (K)
- Amount of Substance (mol)
- Luminous Intensity (cd)
Derived quantities are expressed using combinations of these base units.
Dimensional analysis allows us to:
✔ Check the correctness of equations
✔ Derive formulas
✔ Convert units
✔ Understand which physical quantities are comparable
✔ Solve CUET, JEE, and NEET MCQs quickly
Why CUET, NEET & JEE Love Dimensional Questions
Dimensional Analysis questions test your understanding of:
- How physical formulas are structured
- Whether two quantities can be added or compared
- Which constants have dimensions
- How to derive new relations
CUET especially asks MATCH-LIST and assertion–reason type dimensional questions.
CUET/JEE/NEET PRACTICE SECTION — MCQs WITH OPTIONS + ANSWERS
(1) The dimension of E²/μ₀ in mass (M), length (L) and time (T) is (E = electric field, μ₀ = permeability of free space)
a) [M²L³T-2A-2]
b) [MLT-4]
c) [ML³T-2]
d) [ML⁴T-4]
✔ Answer: b
(2) The dimension of angular momentum in mass (M), length (L) and time (T) is
a) [MLT-1]
b) [ML-1T-1]
c) [ML²T-1]
d) [ML-1T-2]
✔ Answer: c
(3) If E and E₀ represent energies, τ and t₀ represent times, which relation is dimensionally correct?
a) E=E0etE = E₀e^t
b) E=E0t0e−t/t0E = E₀ t₀ e^{-t/t₀}
c) E=E0t0e−t2E = E₀ t₀ e^{-t^2}
d) E=E0e−t/t0E = E₀ e^{-t/t₀}
✔ Answer: d
(4) If E = energy and G = gravitational constant, E/G has dimensions:
a) [M2L-1T0]
b) [ML-1T-1]
c) [ML0T0]
d) [M2L-2T-1]
✔ Answer: a
(5) Dimensions of ε0dϕEdt\varepsilon_0 \frac{d\phi_E}{dt} are same as:
a) Potential
b) Current
c) Charge
d) Capacitance
✔ Answer: b
(6) Quantity with neither units nor dimensions:
a) Relative velocity
b) Relative density
c) Angle
d) Energy
✔ Answer: b
(7) If momentum (P), area (A), time (T) are fundamental quantities, dimensional formula for power is:
a) P1/2AT-1
b) P2AT-2
c) PA1/2T-2
d) PA1T-2
✔ Answer: c
(8) Dimensions of σ b4 (Stefan’s constant × Wien’s constant):
a) [M0L0T0]
b) [ML4T-3]
c) [ML-2T]
d) [ML4T-2]
✔ Answer: b
(9) Dimensional formula of ε0 μ0:
a) [M0L-2T2]
b) [M0L2T-2]
c) [M0LT-1]
d) [M0L-1T]
✔ Answer: a
(10) For P = P₀e^{-at²}, dimension of constant a is
a) dimensionless
b) [T-2]
c) [T2]
d) same as P
✔ Answer: b
(11) Which pair has same dimensions?
a) Force & surface tension
b) Frequency & velocity gradient
c) Angular speed & solid angle
d) Stefan constant & Planck constant
✔ Answer: b
(12) Dimensional formula of AD/B from F = A cos Bx + C sin Dt:
a) [M0LT-1]
b) [ML2T-3]
c) [MLT-2]
d) [M2L2T-3]
✔ Answer: b
(13) In P = a – t² / bx (P = pressure), dimension of a/b is:
a) [LT2]
b) [MT-2]
c) [ML2T-4]
d) [M2LT-2]
✔ Answer: b
(14) Dimensions of stopping potential:
a) [ML-1T-2A3]
b) [M-1L-2T3A2]
c) [M-2LT-3A-1]
d) [ML2T-3A-1]
✔ Answer: d
(15) Not dimensionless:
a) Relative permeability
b) Power factor
c) Permeability of free space
d) Quality factor
✔ Answer: c
(16) With F, L, T as fundamental quantities, dimension of density is:
a) FL-4T2
b) FL-3T2
c) FL-5T2
d) FL-3T3
✔ Answer: a
(17) If (Energy × speed) = [MaLbTc], values of a, b, c are:
a) (1, 3, –3)
b) (1, 2, 3)
c) (1, 2, 3)
d) (1, 3, –2)
✔ Answer: a
(18) Dimensions of Angle × Force × Length:
a) (1, 1, –1)
b) (1, 2, –2)
c) (1, 1, 1)
d) (1, 2, 2)
✔ Answer: b
(19) Dimensional formula of emissivity:
a) [ML0T-3]
b) [ML2T-3]
c) [M0L0T0]
d) [ML2T-2]
✔ Answer: c
(20) Same dimensions:
a) Electric displacement & surface charge density
b) Displacement current & electric field
c) Current density & surface charge density
d) Electric potential & energy
✔ Answer: a
(21) Dimensional formula of viscosity using P, A, T:
a) PA-1T0
b) PAT-2
c) PA-1T
d) PA-1T-1
✔ Answer: a
(22) Same dimensions:
a) Velocity gradient & decay constant
b) Wien constant & Stefan constant
c) Angular frequency & angular momentum
d) Wave number & Avogadro number
✔ Answer: a
(23) Pair with different dimensions:
a) Wave number & Rydberg constant
b) Stress & coefficient of elasticity
c) Coercivity & magnetization
d) Specific heat capacity & latent heat
✔ Answer: d
(24) Dimension of mutual inductance:
a) [ML2T-2A-1]
b) [ML2T-3A-1]
c) [ML2T-2A-2]
d) [ML2T-3A-2]
✔ Answer: c
(25) Dimensions of B2/μ0:
a) [ML2T-2]
b) [MLT-2]
c) [ML-1T-2]
d) [ML2T-2A-1]
✔ Answer: c
(26) Dimension of density in system of C, G, h is:
a) C3G-2h-1
b) C5G-2h-1
c) C-3/2G-1/2h1/2
d) C9/2G-1/2h-1/2
✔ Answer: b
(27) Dimensional formula for power of a lens:
a) [L-1M0T0]
b) [L0M-1T0]
c) [L0M0T-1]
d) [L0M0T0]
✔ Answer: a
(28) Dimensional formula of electric flux:
a) [ML-3T3A-1]
b) [ML3T3A-1]
c) [ML-3T-3A-1]
d) [M-1L3T-3A-1]
✔ Answer: c
(29) Dimensions of Boltzmann constant:
a) [ML2T-2Θ-1]
b) [ML2T-2Θ]
c) [M2LT-2Θ-1]
d) [ML0T-2Θ-1]
✔ Answer: a
(30) Dimension of angular momentum:
a) [M0L1T-1]
b) [ML2T-2]
c) [ML2T-1]
d) [M2L1T-2]
✔ Answer: c
Conclusion
This long-form article combines all major dimensional analysis concepts, includes exam-level MCQs, and integrates CUET, NEET, and JEE targeted keywords. Solving these questions builds confidence and ensures you can handle both direct and tricky dimensional problems in competitive exams.
