1000 drops of same size are charged to a potential of 1 V each. If they coalesce to form in single drop, its potential would be

Options

A. increase
B. remain same
C. decrease
D. depend on size

Answer

To solve the problem, we need to determine the potential of a single drop formed by the coalescence of 1000 smaller drops, each charged to a potential of 1 V.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have 1000 identical small drops, each with a potential of 1 V. When these drops coalesce into a single larger drop, we need to find the potential of this larger drop.

2. **Volume of the Drops**:
The volume \( V \) of a single small drop can be expressed as:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the small drop. Therefore, the total volume of 1000 small drops is:
\[ V_{total} = 1000 \times \frac{4}{3} \pi r^3 = \frac{4000}{3} \pi r^3 \]

3. **Volume of the Larger Drop**:
Let \( R \) be the radius of the larger drop formed by coalescing the 1000 small drops. The volume of the larger drop is:
\[ V_{big} = \frac{4}{3} \pi R^3 \]
Setting the total volume equal to the volume of the larger drop gives:
\[ \frac{4}{3} \pi R^3 = \frac{4000}{3} \pi r^3 \]
Simplifying this, we find:
\[ R^3 = 1000 r^3 \implies R = 10r \]

4. **Charge of the Drops**:
Let \( q \) be the charge of each small drop. The total charge \( Q \) of the larger drop will be:
\[ Q = 1000q \]

5. **Potential of the Small Drops**:
The potential \( V \) of a small drop is given by:
\[ V = k \frac{q}{r} = 1 \text{ V} \]
where \( k \) is Coulomb's constant.

6. **Potential of the Larger Drop**:
The potential \( V_{big} \) of the larger drop can be expressed as:
\[ V_{big} = k \frac{Q}{R} = k \frac{1000q}{10r} = 100 k \frac{q}{r} \]
From the potential of the small drop, we know \( k \frac{q}{r} = 1 \text{ V} \). Therefore:
\[ V_{big} = 100 \times 1 \text{ V} = 100 \text{ V} \]

7. **Conclusion**:
The potential of the larger drop formed by the coalescence of 1000 smaller drops is 100 V.

### Final Answer:
The potential of the larger drop is **100 V**.