Assertion (A): If the distance between two given bodies is halved, the force between them is quadrupled.
Reason (R): In the universe, any two material bodies attract each other with a force which is inversely proportional to the square of the distance between them.

Options

A. Both A and R are correct and R is the correct explanation of A.
B. Both A and R are correct but R is not the correct explanation of A.
C. A is correct and R is incorrect.
D. Both A and R are incorrect.

Explanation

To solve the question, we need to analyze the assertion (A) and the reason (R) provided:

### Step 1: Understand the Assertion (A)
The assertion states that if the distance between two given bodies is halved, the force between them is quadrupled.

### Step 2: Recall the Law of Gravitation
According to Newton's Law of Universal Gravitation, the force (F) between two masses (M1 and M2) is given by the formula:
\[ F = \frac{G \cdot M1 \cdot M2}{R^2} \]
where:
- \( G \) is the gravitational constant,
- \( R \) is the distance between the two masses.

### Step 3: Analyze the Change in Distance
If the distance \( R \) is halved, then the new distance becomes \( \frac{R}{2} \).

### Step 4: Calculate the New Force
Using the new distance in the gravitational force formula:
\[ F' = \frac{G \cdot M1 \cdot M2}{\left(\frac{R}{2}\right)^2} \]
This simplifies to:
\[ F' = \frac{G \cdot M1 \cdot M2}{\frac{R^2}{4}} = 4 \cdot \frac{G \cdot M1 \cdot M2}{R^2} \]
Thus, we find:
\[ F' = 4F \]
This shows that the new force \( F' \) is indeed four times the original force \( F \).

### Step 5: Understand the Reason (R)
The reason states that in the universe, any two material bodies attract each other with a force that is inversely proportional to the square of the distance between them. This is a correct statement as it aligns with the formula we used.

### Conclusion
Both the assertion (A) and the reason (R) are correct, and the reason (R) correctly explains the assertion (A). Therefore, the answer is that both A and R are correct, and R is the correct explanation of A.

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