**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}]

= [M^{0}LT^{-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].[M^{0} 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 L^{2} T^{-2}]

Similarly,

f = 1/t

= 1/[T]

= [T^{-1}]

= [M^{0}L^{0}T^{-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**

**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.**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.**Dimensionless variable:**It is a type of physical quantity that doesn’t have dimension but is variable. For example, angle, specific gravity, relative density.**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 [M^{0}LT^{-1}]

Dimension formula of u is [M^{0}LT^{-1}]

Dimension formula of a.t is [M^{0}LT^{-2}] [T] = [M^{0}LT^{-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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