If the displacement of simple pendulum at any time is 0.02 m and acceleration is `2 m//s^2,`then in this time angular velocity will be

Options

A. `100` rad/s
B. `10` rad/s
C. `1` rad/s
D. `0.1` rad/s

Explanation

To solve the problem of finding the angular velocity of a simple pendulum given its displacement and acceleration, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Displacement (x) = 0.02 m
- Acceleration (a) = 2 m/s²

2. **Use the Formula Relating Acceleration and Angular Velocity:**
In simple harmonic motion (SHM), the linear acceleration (a) is related to the angular velocity (ω) and displacement (x) by the formula:
\[ a = \omega^2 \cdot x \]
Here, we will consider the magnitude of acceleration, so we can drop the negative sign.

3. **Rearrange the Formula to Solve for Angular Velocity (ω):**
We can rearrange the formula to find ω:
\[ \omega^2 = \frac{a}{x} \]
Taking the square root gives us:
\[ \omega = \sqrt{\frac{a}{x}} \]

4. **Substitute the Given Values:**
Now, substitute the given values into the equation:
\[ \omega = \sqrt{\frac{2 \, \text{m/s}^2}{0.02 \, \text{m}}} \]

5. **Calculate the Value:**
First, calculate the fraction:
\[ \frac{2}{0.02} = 100 \]
Now take the square root:
\[ \omega = \sqrt{100} = 10 \, \text{radians/second} \]

6. **Final Result:**
Therefore, the angular velocity (ω) of the simple pendulum is:
\[ \omega = 10 \, \text{rad/s} \]