Which of the following is equal to `1 kgm^(-1) s^(-1)`?

Options

A. 0.01 poise
B. 0.001 poise
C. 1 poise
D. 10 poise

Answer

To solve the question of which of the following is equal to `1 kg m^(-1) s^(-1)`, we will analyze the given options in the context of the unit of viscosity, which is poise.

### Step-by-Step Solution:

1. **Understanding the Unit of Poise**:
- Poise is a unit of dynamic viscosity.
- The definition of 1 poise is `1 g/(cm·s)`.

2. **Converting Poise to SI Units**:
- We need to convert grams to kilograms and centimeters to meters.
- 1 gram (g) = \(10^{-3}\) kilograms (kg).
- 1 centimeter (cm) = \(10^{-2}\) meters (m).

3. **Expressing 1 Poise in SI Units**:
- Therefore, 1 poise can be expressed as:
\[ 1 \text{ poise} = \frac{1 \text{ g}}{\text{cm} \cdot \text{s}} = \frac{10^{-3} \text{ kg}}{10^{-2} \text{ m} \cdot \text{s}} \]

4. **Simplifying the Expression**:
- This simplifies to:
\[ 1 \text{ poise} = \frac{10^{-3} \text{ kg}}{10^{-2} \text{ m} \cdot \text{s}} = \frac{10^{-3}}{10^{-2}} \frac{\text{kg}}{\text{m} \cdot \text{s}} = 10^{-1} \frac{\text{kg}}{\text{m} \cdot \text{s}} = 0.1 \frac{\text{kg}}{\text{m} \cdot \text{s}} \]

5. **Finding the Equivalent of 1 kg m^(-1) s^(-1)**:
- To find how many poise are equivalent to `1 kg m^(-1) s^(-1)`, we can set up the equation:
\[ x \text{ poise} = 1 \text{ kg m}^{-1} \text{s}^{-1} \]
- Since we found that \(1 \text{ poise} = 0.1 \text{ kg m}^{-1} \text{s}^{-1}\), we can write:
\[ x \cdot 0.1 \text{ kg m}^{-1} \text{s}^{-1} = 1 \text{ kg m}^{-1} \text{s}^{-1} \]

6. **Solving for x**:
- Dividing both sides by \(0.1 \text{ kg m}^{-1} \text{s}^{-1}\):
\[ x = \frac{1}{0.1} = 10 \]

7. **Conclusion**:
- Therefore, `1 kg m^(-1) s^(-1)` is equal to `10 poise`.

### Final Answer:
The correct option is **10 poise**.