An electron is moving in a circle of radius 2m with speed 4 m/s . Find the acceleration of the electron

Options

A. `8 m//s^(2)`
B. `4 m//s^(2)`
C. `16 m//s^(2)`
D. `10 m//s^(2)`

Explanation

To find the acceleration of an electron moving in a circle, we can use the formula for centripetal acceleration, which is given by:

\[ a = \frac{v^2}{r} \]

where:
- \( a \) is the centripetal acceleration,
- \( v \) is the speed of the electron,
- \( r \) is the radius of the circular path.

### Step-by-Step Solution:

1. **Identify the given values**:
- Speed of the electron, \( v = 4 \, \text{m/s} \)
- Radius of the circular path, \( r = 2 \, \text{m} \)

2. **Substitute the values into the formula**:
\[ a = \frac{v^2}{r} = \frac{(4 \, \text{m/s})^2}{2 \, \text{m}} \]

3. **Calculate \( v^2 \)**:
\[ v^2 = 4^2 = 16 \, \text{m}^2/\text{s}^2 \]

4. **Substitute \( v^2 \) back into the equation for acceleration**:
\[ a = \frac{16 \, \text{m}^2/\text{s}^2}{2 \, \text{m}} = 8 \, \text{m/s}^2 \]

5. **Final result**:
The acceleration of the electron is \( 8 \, \text{m/s}^2 \).