Gravitational force between a point mass m and M separated by a distance is F. Now if a point mass 2m is placed next to m is contact with it. The force on M due to `m` and the total force on M are

Options

A. 2F, F
B. F, 2F
C. F, 3F
D. F, F

Explanation

To solve the problem, we need to analyze the gravitational forces acting on the mass \( M \) due to the point masses \( m \) and \( 2m \) when they are placed in contact with each other.

### Step-by-Step Solution:

1. **Understanding the Initial Force**:
The gravitational force \( F \) between the point mass \( m \) and the mass \( M \) is given by the formula:
\[ F = \frac{G \cdot m \cdot M}{R^2} \]
where \( G \) is the gravitational constant, \( m \) is the mass of the point mass, \( M \) is the mass of the larger object, and \( R \) is the distance between the centers of the two masses.

**Hint**: Remember that gravitational force is inversely proportional to the square of the distance between the two masses.

2. **Introducing the Second Mass**:
Now, we place a second mass \( 2m \) in contact with the first mass \( m \). The total mass now acting on \( M \) is \( m + 2m = 3m \).

3. **Calculating the New Gravitational Force**:
The new gravitational force \( F' \) acting on \( M \) due to the combined mass \( 3m \) is given by:
\[ F' = \frac{G \cdot (3m) \cdot M}{R^2} \]
Simplifying this, we have:
\[ F' = \frac{3G \cdot m \cdot M}{R^2} \]

4. **Relating the New Force to the Original Force**:
Since the original force \( F \) was:
\[ F = \frac{G \cdot m \cdot M}{R^2} \]
We can express \( F' \) in terms of \( F \):
\[ F' = 3F \]

5. **Conclusion**:
The force on \( M \) due to the mass \( m \) remains \( F \), while the total gravitational force on \( M \) due to both masses \( m \) and \( 2m \) is \( 3F \).

### Final Answer:
- The force on \( M \) due to \( m \) is \( F \).
- The total force on \( M \) due to \( m \) and \( 2m \) is \( 3F \).