The distance between two masses is to be halved. The gravitational force between them will be :

Options

A. Double
B. One-fourth
C. Quadruple
D. Half

Explanation

To solve the problem, we need to understand how the gravitational force between two masses changes when the distance between them is altered.

### Step-by-Step Solution:

1. **Understand the Gravitational Force Formula:**
The formula for gravitational force (F) between two masses (m1 and m2) separated by a distance (r) is given by:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where G is the gravitational constant.

2. **Identify the Change in Distance:**
The problem states that the distance between the two masses is to be halved. If the original distance is \( r \), the new distance will be:
\[ r' = \frac{r}{2} \]

3. **Substitute the New Distance into the Formula:**
We need to find the new gravitational force (F') when the distance is halved. Substituting \( r' \) into the gravitational force formula gives:
\[ F' = \frac{G \cdot m_1 \cdot m_2}{(r/2)^2} \]

4. **Simplify the Equation:**
Simplifying the denominator:
\[ (r/2)^2 = \frac{r^2}{4} \]
Therefore, the new gravitational force becomes:
\[ F' = \frac{G \cdot m_1 \cdot m_2}{\frac{r^2}{4}} = G \cdot m_1 \cdot m_2 \cdot \frac{4}{r^2} \]

5. **Relate the New Force to the Original Force:**
We can express \( F' \) in terms of the original force \( F \):
\[ F' = 4 \cdot \frac{G \cdot m_1 \cdot m_2}{r^2} = 4F \]

6. **Conclusion:**
Thus, when the distance between the two masses is halved, the gravitational force between them becomes four times the original force. Therefore, the answer is:
\[ F' = 4F \]

### Final Answer:
The gravitational force between the two masses will be **4 times** the original gravitational force.

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