The gravitational force between two object is F. It masses of both object are halved without changing distance between them, then the gravitation force would become

Options

A. `F//4`
B. `F//2`
C. `F`
D. `2F`

Explanation

To solve the problem, we will use the formula for gravitational force, which is given by:

\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]

where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between the centers of the two masses.

### Step-by-Step Solution:

1. **Identify the initial conditions**:
Let the masses of the two objects be \( m_1 \) and \( m_2 \). The initial gravitational force between them is given as \( F \).

\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]

2. **Halve the masses**:
According to the problem, both masses are halved. Therefore, the new masses will be:
- New mass of the first object: \( \frac{m_1}{2} \)
- New mass of the second object: \( \frac{m_2}{2} \)

3. **Calculate the new gravitational force**:
The new gravitational force \( F' \) can be calculated using the same formula, substituting the new masses:

\[ F' = \frac{G \cdot \left(\frac{m_1}{2}\right) \cdot \left(\frac{m_2}{2}\right)}{r^2} \]

Simplifying this, we get:

\[ F' = \frac{G \cdot m_1 \cdot m_2}{4 \cdot r^2} \]

4. **Relate the new force to the original force**:
We know that the original force \( F \) is:

\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]

Therefore, we can express \( F' \) in terms of \( F \):

\[ F' = \frac{1}{4} \cdot \frac{G \cdot m_1 \cdot m_2}{r^2} = \frac{F}{4} \]

5. **Conclusion**:
Thus, the new gravitational force when both masses are halved is:

\[ F' = \frac{F}{4} \]

### Final Answer:
The gravitational force would become \( \frac{F}{4} \).

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