Two brass balls of masses 2 kg and 0.5 kg experience a force of attraction of 2 N. When the distance between their centres is doubled. Then the force of attraction is

Options

A. 1/2 N
B. 1/4 N
C. 1 N
D. 2 N

Explanation

To solve the problem step by step, we will use the Universal Law of Gravitation, which states that the gravitational force \( F \) between two masses \( M_1 \) and \( M_2 \) separated by a distance \( R \) is given by the formula:

\[ F = \frac{G \cdot M_1 \cdot M_2}{R^2} \]

where \( G \) is the gravitational constant.

### Step 1: Identify the given values
- Mass of the first brass ball, \( M_1 = 2 \, \text{kg} \)
- Mass of the second brass ball, \( M_2 = 0.5 \, \text{kg} \)
- Initial force of attraction, \( F = 2 \, \text{N} \)

### Step 2: Write the equation for the initial force
Using the formula for gravitational force, we can write:

\[ F = \frac{G \cdot M_1 \cdot M_2}{R^2} \]

Substituting the known values:

\[ 2 = \frac{G \cdot (2) \cdot (0.5)}{R^2} \]

### Step 3: Rearrange to find \( \frac{G \cdot M_1 \cdot M_2}{R^2} \)
From the equation above, we can express \( \frac{G \cdot M_1 \cdot M_2}{R^2} \):

\[ \frac{G \cdot (2) \cdot (0.5)}{R^2} = 2 \]

This simplifies to:

\[ \frac{G}{R^2} = \frac{2 \cdot 2}{1} = 4 \]

### Step 4: Consider the new scenario where the distance is doubled
When the distance between the centers of the two masses is doubled, the new distance \( R' = 2R \).

### Step 5: Write the equation for the new force
The new force \( F' \) can be expressed as:

\[ F' = \frac{G \cdot M_1 \cdot M_2}{(R')^2} = \frac{G \cdot M_1 \cdot M_2}{(2R)^2} \]

### Step 6: Substitute \( R' \) into the equation
This becomes:

\[ F' = \frac{G \cdot M_1 \cdot M_2}{4R^2} \]

### Step 7: Substitute the value of \( \frac{G \cdot M_1 \cdot M_2}{R^2} \)
From the earlier step, we know that \( \frac{G \cdot M_1 \cdot M_2}{R^2} = 4 \). Thus:

\[ F' = \frac{4}{4} = 1 \, \text{N} \]

### Conclusion
The new force of attraction when the distance is doubled is:

\[ F' = 1 \, \text{N} \]