The surface tension of water in C.G.S units is 70 dyne / cm . Its S.I unit is

Options

A. 70N//m
B. `7xx10^(-2)` N//m
C. 0.7N//m
D. `7xx10^(3) N//m`

Answer

To convert the surface tension of water from CGS units to SI units, we will follow these steps:

### Step 1: Understand the given value in CGS units
The surface tension of water is given as 70 dyne/cm.

### Step 2: Convert dynes to newtons
We know that:
1 newton (N) = 10^5 dynes (dyn)

To convert 70 dynes to newtons, we use the conversion factor:
\[ 70 \text{ dyn} = \frac{70}{10^5} \text{ N} = 70 \times 10^{-5} \text{ N} \]

### Step 3: Convert centimeters to meters
We also know that:
1 centimeter (cm) = 10^-2 meters (m)

### Step 4: Combine the conversions
Now, we need to express the surface tension in terms of newtons per meter. The surface tension in SI units can be expressed as:
\[ \text{Surface Tension} = \frac{70 \times 10^{-5} \text{ N}}{1 \text{ cm}} \]
Substituting the conversion for centimeters:
\[ \text{Surface Tension} = \frac{70 \times 10^{-5} \text{ N}}{10^{-2} \text{ m}} = 70 \times 10^{-5} \times 10^{2} \text{ N/m} \]

### Step 5: Simplify the expression
Now, we simplify the expression:
\[ 70 \times 10^{-5} \times 10^{2} = 70 \times 10^{-3} \text{ N/m} \]

### Final Answer
Thus, the surface tension of water in SI units is:
\[ 70 \times 10^{-3} \text{ N/m} = 0.070 \text{ N/m} \]

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