The dimensional formula of light year is :

Options

A. `[L^(-1)]`
B. `[T^(-1)]`
C. `[L]`
D. `[T]`

Explanation

To find the dimensional formula of a light year, we need to understand what a light year represents. A light year is defined as the distance that light travels in one year.

### Step-by-Step Solution:

1. **Understand the Concept of Light Year**:
- A light year is the distance light travels in one year.

2. **Identify the Speed of Light**:
- The speed of light (c) is approximately \(3 \times 10^8\) meters per second. In dimensional terms, the speed of light is represented as:
\[ [c] = L T^{-1} \]
where \(L\) stands for length and \(T\) stands for time.

3. **Determine the Time Duration**:
- One year is the time duration for which we are calculating the distance. We need to express one year in seconds to maintain consistency in units.
- One year is approximately \(365 \times 24 \times 60 \times 60\) seconds, which is \(3.156 \times 10^7\) seconds.

4. **Calculate the Distance**:
- The distance (d) light travels in one year can be calculated using the formula:
\[ d = c \times t \]
- Substituting the dimensions:
\[ [d] = [c] \times [t] = (L T^{-1}) \times T = L \]

5. **Conclusion**:
- Therefore, the dimensional formula of a light year is:
\[ [\text{Light Year}] = L \]

### Final Answer:
The dimensional formula of a light year is \(L\).

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