Physics · Units And Measurements · NEET
Pure numbers like 1/2, 2, or 2 pi are dimensionless. They have dimensions [M^0 L^0 T^0], so they leave no mark on the dimensional formula. Dimensional analysis only balances M, L, and T. It can tell you KE = (constant) x m v^2, but it can never tell you that constant is 1/2. You must get that number from a real derivation or experiment.
No. Dimensional correctness is necessary but not sufficient. For example s = ut and s = ut + 1/2 at^2 are both dimensionally correct because every term is a length, yet only the second is the full formula. A dimensionally wrong equation is surely wrong, but a dimensionally right one may still be missing terms or have a wrong number.
The angle, log, and exponent must be dimensionless, and their whole result is also just a number (dimensionless). So dimensional analysis cannot handle a term like A sin(wt) or e^(-kt) fully. It cannot produce these functions and cannot fix the constants inside them, because dimensions give no information about a plain number.
Work and torque both have dimensions [M L^2 T^-2]. Energy and torque look identical to the dimensional method, so if a formula could contain either, dimensional analysis cannot decide which one belongs. It sees only the M-L-T pattern, not the physical meaning.
When you derive a formula assuming Q = k a^x b^y c^z, you get one equation each for M, L, and T. That is only three equations. If the formula truly depends on more than three quantities, you have more unknown powers than equations, so the system cannot be solved uniquely. The method then fails to give a single answer.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
1) It cannot find dimensionless constants (like 1/2 or 2 pi). 2) It cannot derive formulas containing trigonometric, logarithmic, or exponential functions. 3) It cannot distinguish quantities with the same dimensions (like work and torque). 4) It cannot handle a formula that depends on more than three physical quantities.
It gives T = k sqrt(L/g), which is the correct dependence, but it cannot find that the constant k equals 2 pi. So it gives the form but not the exact number. This is a classic NEET example of the constant-finding limit.
Yes. If the two sides of an equation have different dimensions, the equation is definitely wrong. The reverse is not true: a dimensionally correct equation is not guaranteed to be right.
These functions are defined by infinite series (for example e^x = 1 + x + x^2/2 + ...). Adding a number to a length or a time makes no sense, so the input x must be a pure number. This is why terms like sin(wt) require wt to be dimensionless.
For NEET it is a fast tool to reject wrong options and check unit consistency, which saves time. But NEET also directly tests its limitations, so you must know exactly what it cannot do, not just what it can.
