Explain the dimension of physical quantity.....
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From left to right: the square, the cube and the tesseract. The two-dimensional (2d) square is bounded by one-dimensional (1d) lines; the three-dimensional (3d) cube by two-dimensional areas; and the four-dimensional (4d) tesseract by three-dimensional volumes. For display on a two-dimensional surface such as a screen, the 3d cube and 4d tesseract require projection.
The first four spatial dimensions, represented in a two-dimensional picture.
Two points can be connected to create a line segment.
Two parallel line segments can be connected to form a square.
Two parallel squares can be connected to form a cube.
Two parallel cubes can be connected to form a tesseract.
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.[1][2] Thus a line has a dimension of one because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces.
In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. Ten dimensions are used to describe string theory, eleven dimensions can describe supergravity and M-theory, and the state-space of quantum mechanics is an infinite-dimensional function space.
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.
The first four spatial dimensions, represented in a two-dimensional picture.
Two points can be connected to create a line segment.
Two parallel line segments can be connected to form a square.
Two parallel squares can be connected to form a cube.
Two parallel cubes can be connected to form a tesseract.
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.[1][2] Thus a line has a dimension of one because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces.
In classical mechanics, space and time are different categories and refer to absolute space and time. That conception of the world is a four-dimensional space but not the one that was found necessary to describe electromagnetism. The four dimensions of spacetime consist of events that are not absolutely defined spatially and temporally, but rather are known relative to the motion of an observer. Minkowski space first approximates the universe without gravity; the pseudo-Riemannian manifolds of general relativity describe spacetime with matter and gravity. Ten dimensions are used to describe string theory, eleven dimensions can describe supergravity and M-theory, and the state-space of quantum mechanics is an infinite-dimensional function space.
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.
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The dimension of the units of a derived physical quantity may be defined as the number of times the fundamental units of mass, length and time appear in the physical quantity.In mechanics, there are three fundamental quantities, namely, mass, length and time.The dimensions of a physical quantity are the powers (or exponents) to which the base quantities are raised to represent that quantity.Let the symbols M, L and T respectively denote the units of mass, length and time.These symbols only indicatethe nature of the unit and not its magnitude. Then the dimension of velocity can bewritten as:Similarly, the dimension of area and density are:Area = Length×Breadth = L×L = L2The dimensionof velocity has:*.zero dimension in mass*.1dimension in length*.–1 dimension in timeArea has 2 dimensions of length*.Zero dimension of mass*.Zero dimension of timeDensity has one dimension of mass, -3 dimensions of length and zero dimension of time. The dimension of the units of a derived physical quantity may be defined as the number of times the fundamental unitsof mass, length and time appear in the physical quantity.The expression for velocity obtained above is said to be its dimensional formula.Thus, the dimensional formula for velocity is [M0L T–1].
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