Physics · Units And Measurements · NEET
Write the quantity you want as a product of powers: Q = F^x A^y T^z. This is the standard method because any derived quantity can be built from the chosen base quantities. Then you need to find the numbers x, y and z. To do that, replace F, A and T with their usual dimensions in M, L, T (mass, length, time). Force [F] = M L T^-2, Acceleration [A] = L T^-2, Time [T] = T. Now both sides are in M, L, T and you can match the powers.
Energy = force x distance. Distance is not fundamental here, so build it: distance = (1/2) A T^2, which has dimensions [A][T^2] (the 1/2 is a number, so we ignore it in dimensions). Therefore energy = [F] x [A][T^2] = [F][A][T^2]. This is the exact NEET 2021 answer. The shortcut is: whenever you need a length, use A T^2, because a = length / time^2.
Mass is normally a base quantity, but here F, A, T are the base. Use F = m a, so m = F / a = [F]/[A] = [F][A^-1]. So mass has dimension [F][A^-1][T^0]. Quick check in M-L-T: [F]/[A] = (M L T^-2)/(L T^-2) = M. Correct, it comes out as pure mass.
Momentum p = mass x velocity. Mass = [F][A^-1] (from above). Velocity = acceleration x time = [A][T]. So p = [F][A^-1] x [A][T] = [F][A^0][T] = [F][T]. Check in M-L-T: F x T = (M L T^-2)(T) = M L T^-1, which is the correct dimension of momentum.
Because dimensional analysis only works with products of powers, not sums. Any quantity that can be expressed through the chosen base quantities must be some F^x A^y T^z. Guessing risks missing a factor. The power form turns the problem into three simple equations (one each for the M, L and T powers), which always gives one clean answer for x, y, z.
If force [F], acceleration [A] and time [T] are chosen as the fundamental physical quantities, find the dimensions of energy.
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?
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Only quantities that can be built as a product of powers of the chosen base quantities. Since F, A and T together cover mass, length and time, all mechanical quantities (energy, momentum, power, pressure) can be expressed. Quantities needing charge or temperature cannot, because those are not covered by F, A, T.
Dimensional analysis only tracks units (M, L, T), not pure numbers. Constants such as 1/2 in (1/2)A T^2 or 2 pi have no dimension, so they never appear in a dimensional formula. This is why dimensional methods cannot find numerical constants in a formula.
Since acceleration = length / time^2, one length equals A x T^2. Remember this single fact and you can replace any distance in a formula quickly when F, A, T are fundamental.
In normal problems the base is fixed as M, L, T. Here the base is swapped to F, A, T. The method is the same (write powers, match), but you express the answer using [F], [A], [T] instead of [M], [L], [T]. Always convert F, A, T into M-L-T first to set up the matching equations.
Yes. NEET has directly asked this exact style (NEET 2021 energy question, NEET 2016 length-from-h-c-G question). It tests whether you truly understand dimensions rather than memorising formulae, so one or two marks often come from here.
