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 need to understand how the gravitational force between two masses changes when the masses are halved. The gravitational force \( F \) between two objects is given by the formula:

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

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 1: Write down the initial gravitational force
The initial gravitational force between the two masses is given by:

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

### Step 2: Halve the masses
According to the problem, both masses are halved. Therefore, the new masses will be:

\[ m_1' = \frac{m_1}{2} \quad \text{and} \quad m_2' = \frac{m_2}{2} \]

### Step 3: Write down the new gravitational force
Now, we need to find the new gravitational force \( F' \) when the masses are halved. The new gravitational force can be expressed as:

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

Substituting the new masses into the equation:

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

### Step 4: Simplify the new force equation
Now, simplify the equation:

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

This can be rewritten as:

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

### Step 5: Substitute the initial force
Since we know that \( F = \frac{G \cdot m_1 \cdot m_2}{r^2} \), we can substitute this into our equation for \( F' \):

\[ F' = \frac{1}{4} F \]

### 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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