Question

Define dimensional formula. Give uses of dimensional analysis. Write down the limitations.

Answer 1

Step1: Dimensional formula

1. Dimension formula refers to the fundamental quantities found in a given physical quantity.
2. It is denoted by square brackets.
3. The dimensional formula computes the variation in the powers of the given quantities.
4. The dimensional formula of a quantity is the expression that shows the powers to which the fundamental units must be raised to obtain one unit of that quantity.
5. If $Q$ is the unit of a derived quantity represented by the equation$Q=M^a{L}^b{T}^c$ then $M^a{L}^b{T}^c$ is known as the dimensional formula, and the exponents$a$, $b$, and $c$ are known as the dimensions.

Step2: Uses of dimensional analysis

1. Dimensional analysis is an important aspect of measurement that is used in real-world physics.
2. To ensure that a dimensional equation is consistent
3. Determining the relationship between physical quantities in physical phenomena.
4. Transferring units from one system to another.

Step3: Limitations of Dimensional Analysis

1. It does not reveal anything about the dimensional constant.
2. It is impossible to derive a formula containing trigonometric functions, exponential functions, logarithmic functions, and so on.
3. It does not indicate whether a physical quantity is a scalar or a vector.