The kinetic energy of a body ia 4 joule and its moment of inertia is `2" kg m"^(2)`. Angular momentum is

Options

A. `2"kg m"^(2)//s`
B. `8kg m^(2)//s`
C. `6kg m^(2)//s`
D. `4 kg m^(2)//s`

Answer

To find the angular momentum of a body given its kinetic energy and moment of inertia, we can use the relationship between kinetic energy (KE), moment of inertia (I), and angular momentum (L).

### Step-by-Step Solution:

1. **Identify the given values**:
- Kinetic Energy (KE) = 4 Joules
- Moment of Inertia (I) = 2 kg·m²

2. **Recall the formula for rotational kinetic energy**:
The kinetic energy of a rotating body is given by the formula:
\[ KE = \frac{L^2}{2I} \]
where \( L \) is the angular momentum and \( I \) is the moment of inertia.

3. **Rearrange the formula to solve for angular momentum (L)**:
To find \( L \), we can rearrange the formula:
\[ L^2 = 2 \cdot KE \cdot I \]
Taking the square root gives:
\[ L = \sqrt{2 \cdot KE \cdot I} \]

4. **Substitute the known values into the equation**:
\[ L = \sqrt{2 \cdot 4 \, \text{J} \cdot 2 \, \text{kg·m}^2} \]
\[ L = \sqrt{16 \, \text{kg}^2 \cdot \text{m}^4/\text{s}^2} \]

5. **Calculate the angular momentum**:
\[ L = 4 \, \text{kg·m}^2/\text{s} \]

### Final Answer:
The angular momentum \( L \) is \( 4 \, \text{kg·m}^2/\text{s} \).

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