If `'A'` is areal velocity of a planet of mass `M`, its angular momentum is

Options

A. `M//A`
B. `2MA`
C. `A^(2)M`
D. `AM^(2)`

Explanation

To find the angular momentum of a planet given its areal velocity \( A \) and mass \( M \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand Areal Velocity**: Areal velocity is defined as the rate at which area is swept out by the radius vector of a planet moving around a central body. According to Kepler's second law, this rate of area change \( \frac{dA}{dt} \) is constant.

2. **Relate Areal Velocity to Angular Momentum**: According to Kepler's second law, we have the relationship:
\[ \frac{dA}{dt} = \frac{L}{2M} \]
where \( L \) is the angular momentum and \( M \) is the mass of the planet.

3. **Substitute Areal Velocity**: We know that the areal velocity \( A \) can be represented as:
\[ A = \frac{dA}{dt} \]
Therefore, we can substitute \( A \) into the equation:
\[ A = \frac{L}{2M} \]

4. **Solve for Angular Momentum \( L \)**: Rearranging the equation to solve for \( L \):
\[ L = 2MA \]

5. **Conclusion**: The angular momentum \( L \) of the planet is given by:
\[ L = 2MA \]

### Final Answer:
The angular momentum of the planet is \( L = 2MA \).

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