The linear and angular acceleration of a particle are 10 m/`"sec"^(2)` and 5 rad/`sec^(2)` respectively it will be at a distance from the axis of rotation -

Options

A. 50m
B. `1//2`m
C. 1m
D. 2m

Answer

To solve the problem, we need to find the distance from the axis of rotation (denoted as \( r \)) using the relationship between linear acceleration (\( a \)) and angular acceleration (\( \alpha \)). The relationship is given by the formula:

\[ a = \alpha r \]

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Linear acceleration \( a = 10 \, \text{m/s}^2 \)
- Angular acceleration \( \alpha = 5 \, \text{rad/s}^2 \)

2. **Use the Formula:**
- We know from the relationship \( a = \alpha r \). We can rearrange this formula to solve for \( r \):
\[ r = \frac{a}{\alpha} \]

3. **Substitute the Given Values:**
- Now, we will substitute the values of \( a \) and \( \alpha \) into the equation:
\[ r = \frac{10 \, \text{m/s}^2}{5 \, \text{rad/s}^2} \]

4. **Calculate \( r \):**
- Performing the division:
\[ r = \frac{10}{5} = 2 \, \text{m} \]

5. **Final Answer:**
- The distance from the axis of rotation is \( r = 2 \, \text{m} \).

### Summary:
The distance from the axis of rotation is \( 2 \, \text{m} \).

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