Simulation · Physics · Class 11
Build a quantity from its dimensions
From the lesson Dimensions and dimensional formulae in Units and Measurements. Change the values and watch what happens.
Build a quantity from its dimensionsPhysics · Class 11
The idea behind it
NCERT §1.4, §1.5
- The dimensions of a quantity are the powers to which the base quantities are raised to express it; they describe its nature, not its size.
- Each base quantity is one dimension, written in square brackets: [M] for mass, [L] for length, [T] for time, [A] for electric current, [K] for thermodynamic temperature, [mol] for amount of substance and [cd] for luminous intensity.
- In mechanics every quantity can be written with [M], [L] and [T] alone. Volume is [L³]; force = mass × acceleration is [M L T⁻²].
- Magnitudes do not enter: speed, initial velocity, final velocity and change in velocity all have the same dimensions, [L T⁻¹].
- The dimensional formula shows which base quantities appear and with what powers, zero powers included: volume [M⁰ L³ T⁰], velocity [M⁰ L T⁻¹], acceleration [M⁰ L T⁻²], density [M L⁻³ T⁰].
- A dimensional equation sets a quantity equal to its dimensional formula, for example [F] = [M L T⁻²] or [ρ] = [M L⁻³ T⁰].
- A dimensional formula can be read off from any defining equation: momentum = mass × velocity gives [M L T⁻¹]; work = force × distance gives [M L² T⁻²].