Physical Quantity: Dimension and Classification | Physics Grade XI

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Physical Quantity: Dimension and Classification | Physics Grade XI

Dimension and Classification of Physical Quantity

Dimension of a Physical Quantity:

This is a new concept which is defined as the power to be raised on fundamental units of mass (m), length (l) and time (t) to a unit of physical quantity. The dimension of mass is expressed as [M], length as [L], and time as [T].

  Example:

        velocity = Displacement/Time

                    = [L]/[T]

                    = [LT-1]

                    = [M0LT-1]

Therefore, the Dimension of velocity are 0 in mass, 1 in length, and -1 in time. 

Dimensional Formula:

Dimensional Formula is an expression that shows how and which fundamental units are involved.

Q.No.1 Write the dimensional Formula of Force.

 We know,

      F = m.a

        = [M].[M0 L T-2]

        = [M L T-2]

Q.No.2 Write the dimensional formula of energy and frequency.

 We know,

     W = F * d

         = [M L T-2] * [L]

         = [M L2 T-2]

Similarly,

   f = 1/t

     = 1/[T]

     = [T-1]

     = [M0L0T-1]

Try these questions yourself:

Q.No.3 Write the dimensional formula of power.

Q.No.4 Write the dimensional formula for acceleration.

Classification of Physical Quantity

  1. Dimensional Variable: It is a type of physical quantity that has its own dimension but its value can differ with respect to situations. For example, Work done, Force, etc.
  2. Dimensional Constant: It is a type of physical quantity that has its own dimension and constant magnitude. For example, Universal gravitational constant (G), velocity of light (c), etc.
  3. Dimensionless variable: It is a type of physical quantity that doesn’t have dimension but is variable. For example, angle, specific gravity, relative density.
  4. Dimensionless constant: It is a type of physical quantity that neither has its dimension nor is variable i.e. constant. For example, pure numbers, numeric constant such as π, etc.

Principle of homogeneity: According to the principle of homogeneity, The dimensions of each term on the two side of correct physical relation must be the same. For example:

Let us take a relation, v = u + at

Dimension formula of v is [M0LT-1]

Dimension formula of u is [M0LT-1]

Dimension formula of a.t is [M0LT-2] [T] = [M0LT-1]

Here, for the relation v = u +at, every term has the same dimensional formula on the both sides. Therefore, the given relation is correct. This follows the principle of homogeneity.

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