A planet is revolving about sun in an elliptical orbit. Choose the correct option based on the statements given below, (i) Areal velocity is constant. (ii) Arval velocity is proportional to velocity (iii) When planet is nearest to sun it's speed is maximum, (iv) Planet will move with constant speed. (v) Areal velocity is inversely proportional to velocity.

Options

A. (i) is correct
B. (ii) is correct
C. (iv) is correct
D. (v) is correct

Answer

To solve the problem, we need to analyze each of the statements provided regarding a planet revolving around the Sun in an elliptical orbit. We will use Kepler's laws of planetary motion, particularly the second law, which relates to areal velocity.

### Step-by-Step Solution:

1. **Understanding Areal Velocity**:
- Areal velocity is defined as the area swept out by the line connecting the planet to the Sun in a given time interval. According to Kepler's second law, this area is constant for equal time intervals.
- **Conclusion**: Statement (i) "Areal velocity is constant" is **True**.

2. **Analyzing Areal Velocity and Velocity**:
- Areal velocity is not directly proportional to the orbital velocity of the planet. While the planet's speed changes as it moves along its elliptical path, the areal velocity remains constant.
- **Conclusion**: Statement (ii) "Areal velocity is proportional to velocity" is **False**.

3. **Speed of the Planet at Perihelion**:
- The planet moves fastest when it is closest to the Sun (at perihelion) due to the gravitational pull being stronger and the conservation of angular momentum.
- **Conclusion**: Statement (iii) "When the planet is nearest to the Sun, its speed is maximum" is **True**.

4. **Constant Speed of the Planet**:
- The planet does not move with a constant speed; its speed varies as it travels along its elliptical orbit. It is fastest at perihelion and slowest at aphelion.
- **Conclusion**: Statement (iv) "Planet will move with constant speed" is **False**.

5. **Areal Velocity and Velocity Relationship**:
- Areal velocity is constant and does not change with the planet's velocity. Therefore, it cannot be inversely proportional to velocity.
- **Conclusion**: Statement (v) "Areal velocity is inversely proportional to velocity" is **False**.

### Final Summary of Statements:
- (i) True
- (ii) False
- (iii) True
- (iv) False
- (v) False

### Correct Options:
The correct options based on the analysis are statements (i) and (iii).