The dimensions of a physical quantity are the powers (exponents) to which the seven base quantities are raised to represent that quantity. The seven base dimensions are written in square brackets: length [L], mass [M], time [T], electric current [A], temperature [K], luminous intensity [cd], and amount of substance [mol]. Memory hook: "dimensions = the power tags on M, L, T" — for example speed = length / time = [L T^-1], so it has 1 power of L and -1 power of T.
The dimension of a quantity is just the set of powers written on the seven base quantities. Here [M^1 L^1 T^-2] is the dimension of force: mass to power 1, length to power 1, time to power -2.
Your doubts, answered
Are dimensions the same as units? (this confuses most students)
No. A unit is the standard you measure with (metre, second, kilogram). A dimension is the power of a base quantity that appears in a physical quantity. Example: speed can have units m/s, km/h, or cm/s, but its dimension is always [L T^-1]. So one dimension can have many units, but the dimension itself does not change.
What do the square brackets like [M L T^-2] actually mean?
The square brackets mean 'the dimensions of'. Inside, each letter is a base quantity and its power tells you how many times that base quantity is multiplied. [M L T^-2] means mass to power 1, length to power 1, time to power -2. This is exactly the dimension of force (F = m a = mass x length / time^2).
How many base dimensions exist, and what are their symbols?
There are seven base dimensions: length [L], mass [M], time [T], electric current [A], thermodynamic temperature [K], luminous intensity [cd], and amount of substance [mol]. In most NEET mechanics problems you only need [M], [L] and [T]. Electricity and heat problems add [A] and [K].
Is the 'dimension' the base quantity itself or the power on it?
Both terms are used, but the precise NCERT meaning is: dimensions are the powers to which the base quantities are raised. So when we say 'the dimension of velocity in time is -1', we mean the exponent of T is -1. When we casually say 'the seven dimensions', we mean the seven base quantities [M], [L], [T], [A], [K], [cd], [mol].
Why does time carry a negative power in speed [L T^-1]?
Because speed = distance / time. Dividing by time means time goes to the denominator, and a quantity in the denominator gets a negative power. So [L] / [T] is written as [L T^-1]. The same logic gives acceleration = [L T^-2], since we divide length by time twice.
⚠️ The NEET trap ✗ Plane angle and solid angle have no dimensions, so they must have no units either. ✓ Plane angle (radian) and solid angle (steradian) are dimensionless but they DO have units. Dimensionless does not mean unit-less. NEET 2022 asked exactly this: the answer is 'Units but no dimensions'. 🧠 NTA loves testing whether you confuse 'has no dimensions' with 'has no units'.
Real NEET questions
NEET 2020
Dimensions of stress are:
A · M L^0 T^-2
B · M L^-1 T^-2 ✓
C · M L T^-2
D · M L^2 T^-2
Solution: Stress = force / area. Step 1: dimension of force = m x a = [M][L T^-2] = [M L T^-2]. Step 2: dimension of area = [L^2]. Step 3: stress = [M L T^-2] / [L^2] = [M L^(1-2) T^-2] = [M L^-1 T^-2]. So the correct answer is B.
NEET 2021
If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities, find the dimensions of energy.
A · [F][A][T^-1]
B · [F][A^-1][T]
C · [F][A][T]
D · [F][A][T^2] ✓
Solution: Energy = force x distance. Here force is already a base quantity [F]. Step 1: express distance using A and T. From s = (1/2) A T^2, distance has dimensions [A][T^2]. Step 2: energy = [F] x distance = [F][A][T^2]. So the answer is D.
NEET 2022
The dimensions [M L T^-2 A^-2] belong to the:
A · Magnetic flux
B · Self inductance
C · Magnetic permeability ✓
D · Electric permittivity
Solution: Check magnetic permeability using F = (mu_0 / 4pi)(I1 I2 / d) x length (force between two wires). Rearranged, mu_0 has dimensions force x length / (current^2 x length) = [M L T^-2][L] / ([A^2][L]) = [M L T^-2 A^-2]. This matches, so the answer is C, magnetic permeability.
Solved Units And Measurements NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
What is the simplest definition of dimensions of a physical quantity?
They are the powers to which the seven base quantities (M, L, T, A, K, cd, mol) are raised to represent that quantity. Example: force = [M L T^-2].
Do all physical quantities have dimensions?
No. Ratios like strain, refractive index, plane angle and solid angle are dimensionless because the base quantities cancel out. They may still have units (like radian) but zero powers of M, L and T.
Why are dimensions important for NEET?
Every year NEET asks 1-2 questions on finding or matching dimensions, and dimensions let you check if a formula is correct and convert units without memorising everything. This makes them high-value, low-effort marks.
What is the difference between dimension and dimensional formula?
A dimension is the individual power on a base quantity. The dimensional formula is the full expression showing all base quantities with their powers together, like [M L^-1 T^-2] for pressure. The next concept explains this fully.
