The moments of inertia of two rotating bodies `A` and `B` are `I_A` and `I_B(I_A gt I_B)`. If their angular momenta are equal then.

Options

A. a. Kinetic energy of A = Kinetic energy of B
B. b. Kinetic energy of A > Kinetic energy of B
C. c. Kinetic energy of A < Kinetic energy of B
D. d. Kinetic energy of the two bodies cannot be compared with the given data

Explanation

To solve the problem, we need to analyze the relationship between the moments of inertia, angular momentum, and kinetic energy of the two rotating bodies A and B.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- We have two bodies, A and B.
- Their moments of inertia are \( I_A \) and \( I_B \) respectively, with the condition \( I_A > I_B \).
- Their angular momenta are equal, i.e., \( L_A = L_B \).

2. **Recall the Formula for Angular Momentum**:
- The angular momentum \( L \) of a rotating body is given by the formula:
\[ L = I \cdot \omega \]
where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.

3. **Set Up the Equations for Angular Momentum**:
- For body A:
\[ L_A = I_A \cdot \omega_A \]
- For body B:
\[ L_B = I_B \cdot \omega_B \]
- Since \( L_A = L_B \), we can equate the two expressions:
\[ I_A \cdot \omega_A = I_B \cdot \omega_B \]

4. **Express Angular Velocities in Terms of Each Other**:
- Rearranging the equation gives:
\[ \frac{\omega_A}{\omega_B} = \frac{I_B}{I_A} \]
- Since \( I_A > I_B \), it follows that \( \frac{I_B}{I_A} < 1 \). Therefore, \( \omega_A < \omega_B \).

5. **Kinetic Energy of Each Body**:
- The kinetic energy \( KE \) of a rotating body is given by:
\[ KE = \frac{1}{2} I \omega^2 \]
- For body A:
\[ KE_A = \frac{1}{2} I_A \omega_A^2 \]
- For body B:
\[ KE_B = \frac{1}{2} I_B \omega_B^2 \]

6. **Relate Kinetic Energies Using Angular Velocities**:
- Substitute \( \omega_A \) in terms of \( \omega_B \):
\[ KE_A = \frac{1}{2} I_A \left(\frac{I_B}{I_A} \omega_B\right)^2 = \frac{1}{2} I_A \cdot \frac{I_B^2}{I_A^2} \cdot \omega_B^2 = \frac{I_B^2}{2 I_A} \cdot \omega_B^2 \]
- Thus, we can compare \( KE_A \) and \( KE_B \):
\[ KE_B = \frac{1}{2} I_B \omega_B^2 \]

7. **Compare the Kinetic Energies**:
- Since \( I_A > I_B \) and \( \frac{I_B^2}{I_A} < I_B \) (because \( I_B < I_A \)), it follows that:
\[ KE_B > KE_A \]

### Conclusion:
From the above analysis, we conclude that the kinetic energy of body B is greater than that of body A.

### Final Answer:
The kinetic energy of body B is greater than the kinetic energy of body A.