Five balls numbered 1,2,3,4,and 5 are suspended using separated threads. The balls (1,2),(2,4) and (4,1) show electrostatic attraction while balls (2,3) and (4,5) show repulsion. Therefore, ball 1 must be

Options

A. negatively charged
B. Positively charges
C. neutral
D. made of metal

Explanation

To determine the nature of ball 1 based on the given electrostatic interactions between the balls, we can follow these steps:

### Step 1: Analyze the given interactions
We know the following interactions:
- Balls (1, 2), (2, 4), and (4, 1) show electrostatic attraction.
- Balls (2, 3) and (4, 5) show electrostatic repulsion.

### Step 2: Assign charges based on attraction
Since balls (1, 2), (2, 4), and (4, 1) attract each other, we can assume that:
- If ball 2 is positive (+), then ball 4 must be negative (−) to attract each other.

### Step 3: Analyze ball 1's charge
From the attraction between balls 4 and 1, if ball 4 is negative (−), then ball 1 must be positive (+) to attract ball 4. So far, we have:
- Ball 2: +
- Ball 4: −
- Ball 1: +

### Step 4: Check consistency with other interactions
Now, we check the interaction between balls 1 and 2. If both ball 1 and ball 2 are positive, they should repel each other, not attract. This contradicts the given condition that balls 1 and 2 attract each other.

### Step 5: Consider other charge combinations
We can also try assuming ball 2 is negative (−) and ball 4 is positive (+). However, this leads to the same contradiction with ball 1.

### Step 6: Assume ball 1 is neutral
Since no combination of charges on balls 1, 2, and 4 satisfies all conditions, we can conclude that ball 1 must be neutral. A neutral ball can attract both positive and negative charges, allowing it to attract both ball 2 (if it is positive) and ball 4 (if it is negative).

### Step 7: Verify with remaining interactions
Assuming ball 1 is neutral:
- Ball 2 (positive) can attract ball 1 (neutral).
- Ball 4 (negative) can also attract ball 1 (neutral).
- For balls 2 and 3 to repel, ball 3 must be positive (since 2 is positive).
- For balls 4 and 5 to repel, ball 5 must also be positive (since 4 is negative).

### Conclusion
Thus, the nature of ball 1 must be **neutral**.

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