The surface tension of a liquid is 90 dyne/cm. What is the value in SI system?

Options

A. `9xx10^(-4)N//m`
B. `9xx10^(-2)N//m`
C. `9xx10^(-1)N//m`
D. `9xx10^(2)N//m`

Explanation

To convert the surface tension of a liquid from dyne/cm to the SI unit of Newton/meter, we follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Value**:
The surface tension is given as 90 dyne/cm.

2. **Identify the Conversion Factors**:
- 1 dyne = \(10^{-5}\) Newton
- 1 cm = \(10^{-2}\) meter

3. **Convert dyne to Newton**:
To convert the dyne value to Newton, we multiply by the conversion factor:
\[ 90 \text{ dyne} = 90 \times 10^{-5} \text{ Newton} \]

4. **Convert cm to meter**:
Since the surface tension is given in dyne/cm, we need to convert cm to meters:
\[ 1 \text{ cm} = 10^{-2} \text{ m} \]

5. **Combine the Conversions**:
The surface tension in SI units (Newton/meter) can be calculated as follows:
\[ \text{Surface Tension} = \frac{90 \times 10^{-5} \text{ Newton}}{10^{-2} \text{ m}} = 90 \times 10^{-5} \times 10^{2} \text{ Newton/m} \]

6. **Simplify the Expression**:
\[ = 90 \times 10^{-3} \text{ Newton/m} \]

7. **Final Result**:
\[ = 9 \times 10^{-2} \text{ Newton/m} \]

Thus, the value of the surface tension in the SI system is \(9 \times 10^{-2} \text{ Newton/m}\).