Explain the uses of dimensional equations giving atleast one example in each case.

Explanation

To explain the uses of dimensional equations, we can break down the explanation into four main points, providing an example for each case.

### Step-by-Step Solution:

1. **Checking the Correctness of a Physical Relation**:
- Dimensional equations can be used to verify if a physical equation is dimensionally consistent. This means that both sides of the equation must have the same dimensions.
- **Example**: Consider the equation for the period \( T \) of a simple pendulum, given by \( T = 2\pi \sqrt{\frac{L}{g}} \), where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.
- The dimensions of \( T \) are \([T]\).
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