To calculate the dimensional formula of a physical quantity, you need to express the quantity in terms of its fundamental dimensions. Here's a step-by-step guide on how to do it:

Step 1: Identify the Fundamental Dimensions: The fundamental dimensions are the basic dimensions used to measure all other physical quantities. In the International System of Units (SI), the fundamental dimensions are:

• Length (L)
• Mass (M)
• Time (T)
• Electric Current (I)
• Temperature (θ) [Note: Temperature is often represented as θ or Θ to avoid confusion with time (T).]

Step 2: Write the Physical Quantity in Terms of Fundamental Dimensions: Express the given physical quantity in terms of the fundamental dimensions using their respective unit symbols. For example:

• Velocity (v) = [L][T]^-1 (because velocity is defined as distance divided by time).
• Force (F) = [M][L][T]^-2 (because force is defined as mass times acceleration, and acceleration is [L][T]^-2).
• Energy (E) = [M][L]^2[T]^-2 (because energy is defined as force times distance, and force is [M][L][T]^-2).

Step 3: Combine the Fundamental Dimensions: Combine the fundamental dimensions using multiplication and division to express the dimensional formula of the physical quantity. For example:

• The dimensional formula of velocity (v) is [L][T]^-1.
• The dimensional formula of force (F) is [M][L][T]^-2.
• The dimensional formula of energy (E) is [M][L]²[T]^-2.

Step 4: Simplify the Dimensional Formula: In some cases, you can simplify the dimensional formula by canceling out common dimensions or combining exponents. For example:

• The dimensional formula of acceleration (a) is [L][T]^-2, which can be simplified as [LT]^-2.

It's important to note that dimensional analysis is a powerful tool used in physics to check the correctness of equations and to convert between different units. It helps ensure that physical quantities are mathematically consistent and can be used to derive new relationships between different physical quantities.