Physics · Units And Measurements · NEET
It works because of one simple truth: in any correct physics equation, the left side and the right side describe the same physical quantity, so they must have the same dimensions. Length can only equal length, not time. This rule (called the principle of homogeneity) is what lets you cancel and compare dimensions like algebra symbols. If dimensions on the two sides do not match, the equation is wrong for sure.
No. Unit conversion changes numbers within the same dimension, like turning metres into centimetres. Dimensional analysis studies the deeper structure (M, L, T) of a quantity, not its number. Two quantities can share a unit issue but the real check is dimensions. For NEET, use dimensions to test equations and units to convert values.
No, and this is a common trap. Dimensional analysis can find formulas that are simple products of powers, like T = k√(l/g) for a pendulum. But it cannot find pure numbers (like 2π), and it fails when a formula has plus or minus signs, or trig, log, and exponential functions. So it gives the skeleton of a formula, not the constants.
It means you can multiply, divide, and cancel dimensions the same way you handle x and y in maths. For example, speed = length / time = [L]/[T] = [LT⁻¹]. If two identical dimensions appear in numerator and denominator, they cancel. This is why writing quantities as [M^a L^b T^c] makes checking so fast.
Because addition only makes physical sense between the same kind of thing. You cannot add 5 metres to 3 seconds — the result means nothing. In an equation like v = u + at, every term must reduce to [LT⁻¹]. This 'you can only add same dimensions' idea is the foundation that makes dimensional analysis reliable.
Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?
If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities, find the dimensions of energy.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is a method of using the dimensions (M, L, T) of physical quantities, treated like algebra symbols, to check equations, find units, and derive simple formulas.
NEET regularly asks you to find the dimensions of a combination of constants, check consistency, or derive a relation. These are quick marks if you know the method, and it also helps you catch wrong options fast.
Checking the dimensional consistency of an equation, converting a quantity from one unit system to another, and deriving the form of a relation between quantities.
No. It gives the powers of the quantities but never the dimensionless constant, such as 2π, ½, or any pure number, because pure numbers have no dimensions.
The principle of homogeneity: every term added or equated in a physics equation must have the same dimensions on both sides.
