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 a rotating body, we can use the formula:

\[ L = I \cdot \omega \]

where:
- \( L \) is the angular momentum,
- \( I \) is the moment of inertia,
- \( \omega \) is the angular speed.

### Step 1: Calculate the Moment of Inertia (I)

The moment of inertia \( I \) 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:

\[ I = 10 \, \text{kg} \cdot (0.1 \, \text{m})^2 \]

Calculating \( k^2 \):

\[ (0.1 \, \text{m})^2 = 0.01 \, \text{m}^2 \]

Now substituting back:

\[ I = 10 \, \text{kg} \cdot 0.01 \, \text{m}^2 = 0.1 \, \text{kg} \cdot \text{m}^2 \]

### Step 2: Calculate Angular Momentum (L)

Now that we have the moment of inertia, we can calculate the angular momentum using the angular speed \( \omega \).

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

Substituting the values into the angular momentum formula:

\[ L = I \cdot \omega = 0.1 \, \text{kg} \cdot \text{m}^2 \cdot 10 \, \text{rad/s} \]

Calculating:

\[ L = 1 \, \text{kg} \cdot \text{m}^2/\text{s} \]

### Final Answer

Thus, the angular momentum \( L \) is:

\[ L = 1 \, \text{kg} \cdot \text{m}^2/\text{s} \]

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