A wheel of mass 10 kg has a moment of inertia of ` 160 kg-m^(2)` about its own axis, the radius of gyration will be

Options

A. 10m
B. 8m
C. 6m
D. 4m

Answer

To find the radius of gyration \( k \) of the wheel, we can use the relationship between the moment of inertia \( I \), mass \( m \), and radius of gyration \( k \). The formula is given by:

\[ I = m \cdot k^2 \]

Where:
- \( I \) is the moment of inertia,
- \( m \) is the mass,
- \( k \) is the radius of gyration.

### Step-by-Step Solution:

1. **Identify the given values**:
- Mass \( m = 10 \, \text{kg} \)
- Moment of inertia \( I = 160 \, \text{kg} \cdot \text{m}^2 \)

2. **Substitute the values into the formula**:
\[ 160 = 10 \cdot k^2 \]

3. **Rearrange the equation to solve for \( k^2 \)**:
\[ k^2 = \frac{160}{10} \]

4. **Calculate \( k^2 \)**:
\[ k^2 = 16 \]

5. **Take the square root to find \( k \)**:
\[ k = \sqrt{16} = 4 \, \text{m} \]

### Final Answer:
The radius of gyration \( k \) is \( 4 \, \text{m} \).

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