The K.E. of a body is 3 joule and its moment of inertia is `"6 kg m"^(2)`. Then its angular momentum will be

Options

A. `"3 kg m"^(2)//s`
B. `"4 kg m"^(2)//s`
C. `"5 kg m"^(2)//s`
D. `"6 kg m"^(2)//s`

Explanation

To find the angular momentum of a body given its kinetic energy and moment of inertia, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Formula for Kinetic Energy**:
The kinetic energy (K.E.) of a rotating body is given by the formula:
\[ K.E. = \frac{1}{2} I \omega^2 \]
where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.

2. **Substitute the Given Values**:
We know from the problem that:
- \( K.E. = 3 \, \text{J} \)
- \( I = 6 \, \text{kg m}^2 \)

Substituting these values into the kinetic energy formula gives:
\[ 3 = \frac{1}{2} \times 6 \times \omega^2 \]

3. **Solve for Angular Velocity (\( \omega \))**:
Rearranging the equation to solve for \( \omega^2 \):
\[ 3 = 3 \omega^2 \]
Dividing both sides by 3:
\[ \omega^2 = 1 \]
Taking the square root:
\[ \omega = 1 \, \text{rad/s} \]

4. **Calculate Angular Momentum (\( L \))**:
The angular momentum \( L \) is given by the formula:
\[ L = I \omega \]
Substituting the values of \( I \) and \( \omega \):
\[ L = 6 \times 1 = 6 \, \text{kg m}^2/\text{s} \]

5. **Final Answer**:
Therefore, the angular momentum of the body is:
\[ L = 6 \, \text{kg m}^2/\text{s} \]