All the derived physical quantities can be expressed in terms of some combination of the seven fundamental or base quantities.

**Dimension
of Physical ****Quantities**

All
the derived physical quantities can be expressed in terms of some combination
of the seven fundamental or base quantities. These base quantities are known as
dimensions of the physical world, and are denoted with square bracket [ ]. The
three dimensions in mechanics are [L] for length, [m] for mass and [T] for
time. In electricity, [A] is the dimension of electric current. In
thermodynamics, [K] is the dimension for the temperature. In optics [cd] or [Φ]
is the dimension for luminous intensity. The dimension of amount of substance
is [mol].

The
dimensions of a physical quantity are the powers to which the units of base
quantities are raised to represent a derived unit of that quantity.

For
example,

Hence
the dimensions of velocity are 0 in mass, 1 in length and -1 in time.

Dimensional
formula is an expression which shows how and which of the fundamental units are
required to represent the unit of a physical quantity.

For
example, [M^{0}LT^{−2}] is the dimensional formula of
acceleration.

When
the dimensional formula of a physical quantity is expressed in the form of an
equation, such an equation is known as the dimensional equation.

Example,
acceleration = [M^{0}LT−2]. The dimensional formula of various physical
quantities are tabulated in Table 1.11.

Tags : Dimensional Analysis , 11th Physics : UNIT 1 : Nature of Physical World and Measurement

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11th Physics : UNIT 1 : Nature of Physical World and Measurement : Dimension of Physical Quantities | Dimensional Analysis

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