a body of mass 10 kg and radius of gyration 0.1 m is rotating about an axis. If angular speed is 10 rad/s, then angular momentum will be:

Options

A. `1 kg m^(2)//s`
B. `0.1 kg m^(2)//s`
C. `100kg m^(2)//s`
D. `10kg m^(2)//s`

Answer

To find the angular momentum of the body, we can follow these steps:

### Step 1: Calculate the Moment of Inertia
The moment of inertia (I) of a body can be calculated using the formula:
\[ I = m \cdot k^2 \]
where:
- \( m \) is the mass of the body,
- \( k \) is the radius of gyration.

Given:
- Mass \( m = 10 \, \text{kg} \)
- Radius of gyration \( k = 0.1 \, \text{m} \)

Substituting the values:
\[ I = 10 \cdot (0.1)^2 \]
\[ I = 10 \cdot 0.01 \]
\[ I = 0.1 \, \text{kg} \cdot \text{m}^2 \]

### Step 2: Calculate Angular Momentum
The angular momentum (L) can be calculated using the formula:
\[ L = I \cdot \omega \]
where:
- \( I \) is the moment of inertia,
- \( \omega \) is the angular speed.

Given:
- Angular speed \( \omega = 10 \, \text{rad/s} \)

Substituting the values:
\[ L = 0.1 \cdot 10 \]
\[ L = 1 \, \text{kg} \cdot \text{m}^2/\text{s} \]

### Final Answer
The angular momentum of the body is:
\[ L = 1 \, \text{kg} \cdot \text{m}^2/\text{s} \]

---