Physics · Units And Measurements · NEET
Take each term (everything separated by a + or - sign, and each side of the = sign) and write its dimensional formula on its own. Then compare. If every term reduces to the SAME dimensions, the equation is consistent. Example: v = u + at. [v] = [L T^-1], [u] = [L T^-1], [at] = [L T^-2][T] = [L T^-1]. All three terms are [L T^-1], so it is dimensionally consistent. If any term differed, the equation would be wrong.
Because you can only add or subtract quantities of the same kind. This is the principle of homogeneity of dimensions. You cannot add 5 metres to 3 seconds — the sum is meaningless. In physics, a valid equation like s = ut + (1/2)at^2 works only because ut and (1/2)at^2 both have dimension [L], the same as s. If two terms had different dimensions, adding them would be physically impossible.
No. This is the most important NEET point. Dimensional consistency is only a preliminary test. It can catch a wrong equation, but it cannot prove an equation is right. For example, s = ut + at^2 (without the 1/2) is dimensionally consistent but numerically wrong, because dimensional analysis is blind to pure numbers like 1/2, 2, or pi. So: dimensionally wrong = definitely wrong; dimensionally correct = maybe correct.
The quantity inside these functions (the argument) must be dimensionless. So in sin(wt), the product wt must be dimensionless; that forces [w] = [T^-1]. In e^(-kt), kt must be dimensionless. If an exam gives you F = a sin(bt), you can immediately find [b] = [T^-1] because bt must be a pure number. NEET loves to test this.
Yes, and this is a common NEET use. In F = alpha*t + beta*t^2, each term must have the dimension of force [M L T^-2]. So [alpha] = [M L T^-2]/[T] = [M L T^-3] and [beta] = [M L T^-2]/[T^2] = [M L T^-4]. Once you know each term equals force, you solve for the constants term by term.
A force is defined by F = alpha*t + beta*t^2, where t is time and alpha and beta are constants. The factor which is dimensionless is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The principle of homogeneity of dimensions: in a physically correct equation, every term that is added or subtracted, and both sides of the equation, must have identical dimensions. If not, the equation cannot be correct.
No. Consistency is only a necessary condition, not a sufficient one. A wrong equation can still be dimensionally consistent because dimensional analysis ignores pure numbers and dimensionless factors.
It lets you quickly reject wrong options, find the dimensions of unknown constants inside an equation, and check formulas you are unsure about during the exam — all without memorising every derivation.
No. You can only add or subtract quantities that have the same dimensions, just as you can add metres to metres but not metres to seconds. This is the core rule of dimensional consistency.
The argument (the quantity inside the function) must be dimensionless. For example, in sin(wt) the product wt must be a pure number, which forces the angular frequency w to have dimension [T^-1].
