Let A be the Area Swept by the line joining the earth and the sun during Feb-2007. The Area Swept by the same line during the first week of that month is

Options

A. `A//4`
B. `(7A)/29`
C. A
D. `(7A)/30`

Answer

To solve the problem, we will use Kepler's law which states that a planet sweeps out equal areas in equal times.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We need to find the area swept by the line joining the Earth and the Sun during the first week of February 2007. We are given that the total area swept during the entire month of February is \( A \).

2. **Determine the Total Days in February**:
February typically has 28 days (assuming it is not a leap year).

3. **Calculate the Area Swept Per Day**:
Since the area swept is uniform over time, we can find the area swept per day by dividing the total area \( A \) by the number of days in February:
\[ \text{Area swept per day} = \frac{A}{28} \]

4. **Calculate the Area Swept in the First Week**:
The first week consists of 7 days. Therefore, the area swept in the first week can be calculated by multiplying the area swept per day by 7:
\[ \text{Area swept in the first week} = 7 \times \left(\frac{A}{28}\right) = \frac{7A}{28} = \frac{A}{4} \]

5. **Final Answer**:
Thus, the area swept by the line joining the Earth and the Sun during the first week of February 2007 is:
\[ \frac{A}{4} \]