If year is taken as the unit of time and velocity of light as the unit of velocity what is the unit of length ?

Explanation

To find the unit of length when the year is taken as the unit of time and the velocity of light is taken as the unit of velocity, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between units**:
The unit of length can be derived from the formula:
\[ \text{Unit of Length} = \text{Unit of Velocity} \times \text{Unit of Time} \]

2. **Identify the units given**:
- The unit of velocity is given as the velocity of light, which is approximately \(3 \times 10^8\) meters per second.
- The unit of time is given as 1 year.

3. **Convert 1 year into seconds**:
To convert years into seconds, we use the following conversions:
- 1 year = 365 days (approximately)
- 1 day = 24 hours
- 1 hour = 60 minutes
- 1 minute = 60 seconds

Therefore, we can calculate:
\[ 1 \text{ year} = 365 \text{ days} \times 24 \text{ hours/day} \times 60 \text{ minutes/hour} \times 60 \text{ seconds/minute} \]
\[ 1 \text{ year} = 365 \times 24 \times 60 \times 60 \text{ seconds} \]
\[ 1 \text{ year} = 31,536,000 \text{ seconds} \quad (\text{or } 3.1536 \times 10^7 \text{ seconds}) \]

4. **Substitute the values into the formula**:
Now substituting the values into the length formula:
\[ \text{Unit of Length} = (3 \times 10^8 \text{ m/s}) \times (3.1536 \times 10^7 \text{ s}) \]

5. **Calculate the unit of length**:
\[ \text{Unit of Length} = 3 \times 10^8 \times 3.1536 \times 10^7 \text{ m} \]
\[ = 9.4608 \times 10^{15} \text{ m} \]

6. **Interpret the result**:
The result \(9.4608 \times 10^{15} \text{ m}\) is known as one light year, which is the distance that light travels in one year.

### Final Answer:
The unit of length is one light year, which is approximately \(9.46 \times 10^{15}\) meters.

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