An experiment measures quantites `a, b, c` and `X` is calculated from the formula
`X = (ab^(2))/(c^(3))`
If the percentage errors in `a,b,c` are `+- 1%, +- 3%, +- 2%` respectively, the perentage error in `X` can be

Options

A. Several droplets are between the plates at one time, and they would all feel the same force.
B. The cells in the solution have net charges that would affect the droplet charge.
C. A droplet with a net charge would always experience a net force between the plates.
D. A droplet with a net charge would not always experience a net force between the plates.

Explanation

To solve the problem, we need to find the percentage error in the quantity \( X \) calculated from the formula:

\[ X = \frac{ab^2}{c^3} \]

Given the percentage errors in \( a, b, \) and \( c \) are \( \pm 1\% \), \( \pm 3\% \), and \( \pm 2\% \) respectively, we can use the formula for the propagation of errors.

### Step 1: Write down the formula for percentage error in \( X \)

The general formula for the percentage error in a function of multiple variables is given by:

\[ \frac{\Delta X}{X} \times 100 = \frac{\Delta a}{a} \times 100 + n \cdot \frac{\Delta b}{b} \times 100 - m \cdot \frac{\Delta c}{c} \times 100 \]

where \( n \) and \( m \) are the powers of \( b \) and \( c \) in the formula for \( X \). Here, \( n = 2 \) (since \( b \) is squared) and \( m = 3 \) (since \( c \) is cubed).

### Step 2: Substitute the known values into the formula

Substituting the percentage errors:

- For \( a \): \( \frac{\Delta a}{a} \times 100 = \pm 1\% \)
- For \( b \): \( \frac{\Delta b}{b} \times 100 = \pm 3\% \)
- For \( c \): \( \frac{\Delta c}{c} \times 100 = \pm 2\% \)

The formula becomes:

\[ \frac{\Delta X}{X} \times 100 = \pm 1\% + 2 \cdot (\pm 3\%) - 3 \cdot (\pm 2\%) \]

### Step 3: Calculate the total percentage error

Now we can calculate:

\[ \frac{\Delta X}{X} \times 100 = \pm 1\% + 2 \cdot \pm 3\% - 3 \cdot \pm 2\% \]

Calculating each term:

1. \( \pm 1\% \)
2. \( 2 \cdot \pm 3\% = \pm 6\% \)
3. \( -3 \cdot \pm 2\% = \mp 6\% \)

Now, combine these:

\[ \frac{\Delta X}{X} \times 100 = \pm 1\% + \pm 6\% - \mp 6\% \]

This simplifies to:

\[ \frac{\Delta X}{X} \times 100 = \pm 1\% + \pm 6\% + \pm 6\% = \pm 1\% + \pm 12\% \]

Thus, the total percentage error in \( X \) is:

\[ \frac{\Delta X}{X} \times 100 = \pm 13\% \]

### Final Result

The percentage error in \( X \) can be:

\[ \pm 13\% \]