A drop of water of radius `10^(-5) m` is falling through a medium whose density is` 1.21 kg m^(-3)` and coefficient of Viscosity `1.8xx10^(-4)` poise. Find the terminal velocity of the drop.

Explanation

To find the terminal velocity of a water drop falling through a medium, we can use the formula for terminal velocity \( V_t \):

\[ V_t = \frac{2 r^2 (\rho - \sigma) g}{9 \eta} \]

Where:
- \( r \) = radius of the drop
- \( \rho \) = density of the fluid (water)
- \( \sigma \) = density of the medium
- \( g \) = acceleration due to gravity
- \( \eta \) = coefficient of viscosity

### Step-by-Step Solution

1. **Identify the given values:**
- Radius of the drop, \( r = 10^{-5} \, \text{m} \)
- Density of water, \( \rho = 1000 \, \text{kg/m}^3 \)
- Density of the medium, \( \sigma = 1.21 \, \text{kg/m}^3 \)
- Acceleration due to gravity, \( g = 9.8 \, \text{m/s}^2 \)
- Coefficient of viscosity, \( \eta = 1.8 \times 10^{-4} \, \text{poise} \)

2. **Convert the coefficient of viscosity from poise to SI units:**
- \( 1 \, \text{poise} = 0.1 \, \text{Pa.s} \)
- Therefore, \( \eta = 1.8 \times 10^{-4} \, \text{poise} = 1.8 \times 10^{-4} \times 0.1 \, \text{Pa.s} = 1.8 \times 10^{-5} \, \text{Pa.s} \)

3. **Substitute the values into the terminal velocity formula:**
\[ V_t = \frac{2 (10^{-5})^2 (1000 - 1.21) (9.8)}{9 (1.8 \times 10^{-5})} \]

4. **Calculate the numerator:**
- Calculate \( 10^{-5} \) squared:
\[ (10^{-5})^2 = 10^{-10} \]
- Calculate \( 1000 - 1.21 = 998.79 \)
- Now calculate the entire numerator:
\[ 2 \times 10^{-10} \times 998.79 \times 9.8 \approx 1.961 \times 10^{-6} \]

5. **Calculate the denominator:**
\[ 9 \times (1.8 \times 10^{-5}) = 1.62 \times 10^{-4} \]

6. **Now divide the numerator by the denominator to find \( V_t \):**
\[ V_t = \frac{1.961 \times 10^{-6}}{1.62 \times 10^{-4}} \approx 0.0121 \, \text{m/s} \]

7. **Convert the terminal velocity to cm/s if needed:**
\[ V_t \approx 0.0121 \, \text{m/s} = 1.21 \, \text{cm/s} \]

### Final Answer:
The terminal velocity of the drop is approximately \( 0.0121 \, \text{m/s} \) or \( 1.21 \, \text{cm/s} \).