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
- 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 [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.
Share on Social Media