Assertion : Areal velocity of a planet around of surface area and density is same for two planets, escape velocities will be same for both
Reason : Areal velocity `= (L)/(2m)`, Where L is angular momentum of planet about centre of sun.

Options

A. If both Assertin and Reason are correct and Reason is the correct explanation of Assertion
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion
C. If Assertion is true but Reason is false
D. If Assertion is false but Reason is true

Explanation

To solve the assertion and reason question, we need to analyze both statements carefully.

### Step-by-Step Solution:

1. **Understanding Areal Velocity**:
- Areal velocity (A) is defined as the rate at which a planet sweeps out area as it orbits around the sun. Mathematically, it is given by:
\[ A = \frac{L}{2m} \]
- Here, \(L\) is the angular momentum of the planet about the center of the sun, and \(m\) is the mass of the planet.

2. **Escape Velocity**:
- The escape velocity (\(v_e\)) from the surface of a planet is given by the formula:
\[ v_e = \sqrt{\frac{2GM}{R}} \]
- Where \(G\) is the gravitational constant, \(M\) is the mass of the planet, and \(R\) is the radius of the planet.

3. **Analyzing the Assertion**:
- The assertion states that if the areal velocity and density are the same for two planets, then their escape velocities will also be the same.
- However, the escape velocity depends on the mass of the planet (\(M\)) and its radius (\(R\)). Even if the areal velocity is the same, the masses and radii of the planets can differ, leading to different escape velocities.

4. **Analyzing the Reason**:
- The reason provided states that areal velocity is defined as \(A = \frac{L}{2m}\). This is true, as it describes the relationship between areal velocity, angular momentum, and mass.
- It is important to note that angular momentum \(L\) depends on the mass and radius of the planet, but the escape velocity depends on the mass and radius as well. Thus, while the relationship holds, it does not imply that escape velocities will be the same.

5. **Conclusion**:
- The assertion is **false** because the escape velocities can differ even if the areal velocities are the same.
- The reason is **true** as it correctly describes the formula for areal velocity.

### Final Answer:
- Assertion: False
- Reason: True