A square plate of 0.1 m side moves parallel to a second plate with a velocity of `0.1 m//s`, both plates being immersed in water. If the viscous force is 0.002 N and the coefficient of viscosity is 0.01 poise , distance between the plates in m is

Options

A. `0.1`
B. `0.05`
C. `0.005`
D. `0.0005`

Answer

To solve the problem step by step, we will use the formula for viscous force in a fluid between two parallel plates. The formula is given by:

\[ F = \eta A \frac{\Delta V}{\Delta x} \]

Where:
- \( F \) is the viscous force,
- \( \eta \) is the coefficient of viscosity,
- \( A \) is the area of the plate,
- \( \Delta V \) is the difference in velocity between the plates,
- \( \Delta x \) is the distance between the plates.

### Step 1: Calculate the area of the square plate

The area \( A \) of a square plate is calculated using the formula:

\[ A = \text{side}^2 \]

Given that the side of the plate is \( 0.1 \, \text{m} \):

\[ A = (0.1 \, \text{m})^2 = 0.01 \, \text{m}^2 \]

### Step 2: Convert the coefficient of viscosity to SI units

The coefficient of viscosity is given as \( 0.01 \, \text{poise} \). To convert poise to SI units (Pascal-seconds), we use the conversion:

\[ 1 \, \text{poise} = 0.1 \, \text{Pa.s} \]

Thus,

\[ \eta = 0.01 \, \text{poise} = 0.01 \times 0.1 \, \text{Pa.s} = 0.001 \, \text{Pa.s} \]

### Step 3: Identify the difference in velocity

The difference in velocity \( \Delta V \) is given as:

\[ \Delta V = 0.1 \, \text{m/s} \]

### Step 4: Substitute values into the viscous force formula

We have:

- \( F = 0.002 \, \text{N} \)
- \( \eta = 0.001 \, \text{Pa.s} \)
- \( A = 0.01 \, \text{m}^2 \)
- \( \Delta V = 0.1 \, \text{m/s} \)

Substituting these values into the formula:

\[ 0.002 = 0.001 \times 0.01 \times \frac{0.1}{\Delta x} \]

### Step 5: Solve for \( \Delta x \)

Rearranging the equation to solve for \( \Delta x \):

\[ \Delta x = 0.001 \times 0.01 \times \frac{0.1}{0.002} \]

Calculating the right-hand side:

\[ \Delta x = \frac{0.000001}{0.002} = 0.0005 \, \text{m} \]

### Final Answer

The distance between the plates is:

\[ \Delta x = 0.0005 \, \text{m} \]

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