The surface energy of a liquid drop is `E`. It is sprayed into `1000` equal droplets.
the work done in spraying is:

Options

A. 999 E
B. 99 E
C. 9E
D. E

Explanation

To solve the problem of calculating the work done in spraying a liquid drop with surface energy \( E \) into 1000 equal droplets, we can follow these steps:

### Step 1: Understand the Surface Energy of a Liquid Drop
The surface energy \( E \) of a liquid drop is given by the formula:
\[ E = 4\pi r^2 \gamma \]
where \( r \) is the radius of the original drop and \( \gamma \) is the surface tension of the liquid.

### Step 2: Apply Volume Conservation
When the original drop is divided into 1000 smaller droplets, the volume of the original drop must equal the total volume of the smaller droplets. The volume of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
Let the radius of each smaller droplet be \( r' \). Thus, we have:
\[ \frac{4}{3} \pi r^3 = 1000 \cdot \frac{4}{3} \pi (r')^3 \]
This simplifies to:
\[ r^3 = 1000 (r')^3 \]

### Step 3: Solve for the Radius of Smaller Droplets
From the equation \( r^3 = 1000 (r')^3 \), we can find the radius of the smaller droplets:
\[ (r')^3 = \frac{r^3}{1000} \]
Taking the cube root of both sides, we get:
\[ r' = \frac{r}{10} \]

### Step 4: Calculate the Surface Energy of One Smaller Droplet
Now, we can calculate the surface energy of one of the smaller droplets using the new radius \( r' \):
\[ E' = 4\pi (r')^2 \gamma = 4\pi \left(\frac{r}{10}\right)^2 \gamma = 4\pi \frac{r^2}{100} \gamma = \frac{E}{100} \]

### Step 5: Calculate the Total Surface Energy of All Smaller Droplets
Since there are 1000 smaller droplets, the total surface energy \( E_{total} \) of all the droplets is:
\[ E_{total} = 1000 \cdot E' = 1000 \cdot \frac{E}{100} = 10E \]

### Step 6: Calculate the Work Done
The work done in spraying the original drop into smaller droplets is equal to the change in surface energy. The initial surface energy was \( E \) and the final surface energy after spraying is \( 10E \):
\[ \text{Work Done} = E_{total} - E = 10E - E = 9E \]

### Final Answer
Thus, the work done in spraying the liquid drop into 1000 equal droplets is:
\[ \boxed{9E} \]