If the area swept by the line joining the sun and the earth from Feb 1 to Feb 7 is ‘A’, then the area swept by the radius vector from Feb 8 to Feb 28 is

Options

A. A
B. `2A`
C. `3A`
D. `4A`

Answer

To solve the problem, we will use Kepler's Second Law of Planetary Motion, which states that a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.

### Step-by-Step Solution:

1. **Identify the Time Intervals:**
- The first time interval is from February 1 to February 7, which is 7 days.
- The second time interval is from February 8 to February 28, which is 21 days.

2. **Area Swept in the First Interval:**
- The area swept by the line joining the Sun and the Earth from February 1 to February 7 is given as 'A'.

3. **Calculate the Area Swept per Day:**
- To find the area swept in one day, we divide the total area 'A' by the number of days (7 days):
\[ \text{Area per day} = \frac{A}{7} \]

4. **Calculate the Area Swept in the Second Interval:**
- For the second interval (February 8 to February 28), which is 21 days, we can calculate the total area swept as follows:
\[ \text{Area for 21 days} = \text{Area per day} \times 21 = \left(\frac{A}{7}\right) \times 21 \]

5. **Simplify the Expression:**
- Simplifying the above expression:
\[ \text{Area for 21 days} = \frac{A \times 21}{7} = 3A \]

6. **Final Result:**
- Therefore, the area swept by the radius vector from February 8 to February 28 is \(3A\).

### Final Answer:
The area swept by the radius vector from February 8 to February 28 is \(3A\).

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