Question

What do we mean by dimension ?

Answer 1

Normaly we write dimensional formula that is totally different MLT that is different Sincethe question is about the definition of 'Dimension' In physics and mathematics, thedimensionof a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. to give you a physical 'sense' of Dimensions, an informal definition would be that a dimension is a measurable and state-able physical quantity that gives us information about the state of a system. For example, if you want to locate an object in 3D space, you would need the x-coordinate, the y-coordinate and the z-coordinate. The x, y, z coordinates are nothing but dimensions for that particular object. Similarly, if you wanted to specify the position of an object and the time when the object was at that position(objects move around!), then you would have to specify the time-coordinate, t in addition to the x, y, z coordinates. We say a system is n-dimentional if there are n physical quantities whichcompletelydefine the state of the system. If you're concerned with point particles moving around in 3D space, the only dimensions you need are x, y, z, and t coordinates foreachparticle. So for 1 particle only we can say our system is 4D or 4-diamensional. The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur in mathematics and the sciences. They may be parameter spaces or configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in. which implies that position coordinates aren't theonlydimensions. For example, if a system consisting of homogenous ideal gas particles following the postulates of Kinetic Theory of Gases contained in an ideal confinement, the Pressure, P; Volume, V; Temperature, T; and amount of gas i.e no. of moles, n; are the only requires dimensions to state all the properties of that system. I hope this answers your question.