Five Styrofoam balls are suspended from insulating threads. Several experiments are performed on the balls and the following observations are made:
(i) Ball A repels C and attracts B.
(ii) Ball D attracts B and has no effect on E.
(iii) A negatively charged rod attracts both A and E.
An electrically neutral Styrofoam ball gets attracted if placed nearby a charged body due to induced charge. What are the charges, if any, on each ball A,B,C,D, and E?

Options

A. `+, -, + , 0, + `
B. `+, -, +, +, 0`
C. `-, +, - , 0, 0`
D. `+, - , +, 0, 0`

Explanation

To determine the charges on each of the Styrofoam balls A, B, C, D, and E based on the observations provided, we can analyze each observation step by step.

### Step-by-Step Solution:

1. **Observation (i): Ball A repels C and attracts B.**
- Since A repels C, both A and C must have the same type of charge (either both positive or both negative).
- Since A attracts B, A and B must have opposite charges. Therefore, if A is positive, B must be negative, and vice versa.

2. **Observation (ii): Ball D attracts B and has no effect on E.**
- Since D attracts B, D and B must have opposite charges. If B is negative, D must be positive, and if B is positive, D must be negative.
- The fact that D has no effect on E means that E is electrically neutral (no charge).

3. **Observation (iii): A negatively charged rod attracts both A and E.**
- A negatively charged rod attracts A, which indicates that A must be positively charged (since opposite charges attract).
- Since E is neutral, it can be attracted by the negatively charged rod due to induced charge. This means that E remains neutral but can be influenced by the presence of the negative charge.

### Conclusion:
From the analysis:
- Since A is positively charged (attracted by the negatively charged rod), C must also be positively charged (since A repels C).
- B must be negatively charged (since A attracts B).
- D must be positively charged (since it attracts B, which is negative).
- E is neutral (no charge).

Thus, the charges on the balls are:
- **Ball A: Positive (+)**
- **Ball B: Negative (-)**
- **Ball C: Positive (+)**
- **Ball D: Positive (+)**
- **Ball E: Neutral (0)**

### Summary of Charges:
- A: +
- B: -
- C: +
- D: +
- E: 0