The surface tension of a liquid is `10^(8)` dyne/cm .It is equivalent to

Options

A. `10^(7) Nm^(-1)`
B. `10^(5)Nm^(-1)`
C. `10^(4)Nm^(-1)`
D. `10^(6)Nm^(-1)`

Explanation

To convert the surface tension from dyne/cm to newton/m, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given value**:
The surface tension of the liquid is given as \( T = 10^8 \) dyne/cm.

2. **Convert dyne to newton**:
We know that:
\[ 1 \text{ Newton} = 10^5 \text{ dyne} \]
Therefore, to convert dyne to newton, we divide the value in dyne by \( 10^5 \):
\[ T_{\text{newton}} = \frac{T_{\text{dyne}}}{10^5} = \frac{10^8 \text{ dyne}}{10^5} = 10^{8-5} = 10^3 \text{ N} \]

3. **Convert cm to m**:
We also know that:
\[ 1 \text{ cm} = 10^{-2} \text{ m} \]
Therefore, to convert cm to m, we multiply the value in cm by \( 100 \) (or \( 10^2 \)):
\[ T_{\text{m}} = T_{\text{newton}} \times 100 = 10^3 \text{ N} \times 100 = 10^3 \text{ N} \times 10^2 = 10^5 \text{ N/m} \]

4. **Final Result**:
Thus, the surface tension in newton per meter is:
\[ T = 10^5 \text{ N/m} \]

### Conclusion:
The surface tension of the liquid is equivalent to \( 10^5 \) newton/m.

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