Four identical metallic objects carry the following charges : +1.6, +6.2, -4.8 and `-9.4 mu C`. The object are brought simultaneously into contact, so that each touches the others. Then they are separated, what is the final charge on each object ?

Options

A. `-6.4 mu C`
B. `-1.6 mu C`
C. `-5.6 mu C`
D. `-2.4 mu C`

Answer

To solve the problem of finding the final charge on each of the four identical metallic objects after they are brought into contact and then separated, we can follow these steps:

### Step 1: Identify the charges on the objects
The charges on the four identical metallic objects are:
- Object 1: +1.6 µC
- Object 2: +6.2 µC
- Object 3: -4.8 µC
- Object 4: -9.4 µC

### Step 2: Calculate the total charge
To find the total charge, we sum the individual charges:
\[ \text{Total Charge} = (+1.6) + (+6.2) + (-4.8) + (-9.4) \]

Calculating this step-by-step:
1. \(1.6 + 6.2 = 7.8\)
2. \(7.8 - 4.8 = 3.0\)
3. \(3.0 - 9.4 = -6.4\)

Thus, the total charge is:
\[ \text{Total Charge} = -6.4 \, \mu C \]

### Step 3: Determine the final charge on each object
Since the objects are identical and they will share the total charge equally when brought into contact, we divide the total charge by the number of objects (4):
\[ \text{Final Charge on each object} = \frac{\text{Total Charge}}{4} = \frac{-6.4 \, \mu C}{4} \]

Calculating this gives:
\[ \text{Final Charge on each object} = -1.6 \, \mu C \]

### Conclusion
After the objects are brought into contact and then separated, the final charge on each object is:
\[ \text{Final Charge} = -1.6 \, \mu C \]

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