A new system of unit is evolved in which the values of `mu_(0)` and `in_(0)` are 2 and 8 respectively. Then the speed of light in this system will be

Options

A. 0.25
B. 0.5
C. 0.75
D. 1

Explanation

To find the speed of light in the new system of units where the values of \(\mu_0\) and \(\epsilon_0\) are given as 2 and 8 respectively, we can use the formula for the speed of light \(c\):

\[ c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \]

### Step-by-step Solution:

1. **Identify the values**:
- Given \(\mu_0 = 2\)
- Given \(\epsilon_0 = 8\)

2. **Substitute the values into the formula**:
\[ c = \frac{1}{\sqrt{2 \times 8}} \]

3. **Calculate the product inside the square root**:
\[ 2 \times 8 = 16 \]

4. **Take the square root**:
\[ \sqrt{16} = 4 \]

5. **Calculate the speed of light**:
\[ c = \frac{1}{4} \]

6. **Convert to decimal form**:
\[ c = 0.25 \]

Thus, the speed of light in this new system of units is \(0.25\).

### Final Answer:
The speed of light in this system is \(0.25\).

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