Two bodies with moment of inertia `I_1` and `I_2 (I_1 gt I_2)` have equal angular momenta. If their kinetic energy of rotation are `E_1` and `E_2` respectively, then.

Options

A. `E_(1)=E_(2)`
B. `E_(1)ltE_(2)`
C. `E_(1)gtE_(2)`
D. `E_(1)geE_(2)`

Explanation

To solve the problem, we need to analyze the relationship between the moment of inertia, angular momentum, and kinetic energy of rotation for two bodies.

### Step-by-Step Solution:

1. **Understanding Angular Momentum**:
- The angular momentum \( L \) of a rotating body is given by the formula:
\[ L = I \omega \]
- Where \( I \) is the moment of inertia and \( \omega \) is the angular velocity.

2. **Given Conditions**:
- We have two bodies with moments of inertia \( I_1 \) and \( I_2 \) such that \( I_1 > I_2 \).
- It is given that both bodies have equal angular momentum:
\[ L_1 = L_2 \]

3. **Expressing Angular Velocities**:
- From the angular momentum formula, we can express the angular velocities in terms of angular momentum:
\[ \omega_1 = \frac{L_1}{I_1} \quad \text{and} \quad \omega_2 = \frac{L_2}{I_2} \]
- Since \( L_1 = L_2 \), we can denote this common angular momentum as \( L \):
\[ \omega_1 = \frac{L}{I_1} \quad \text{and} \quad \omega_2 = \frac{L}{I_2} \]

4. **Kinetic Energy of Rotation**:
- The kinetic energy \( E \) of a rotating body is given by:
\[ E = \frac{1}{2} I \omega^2 \]
- For the two bodies, we can write:
\[ E_1 = \frac{1}{2} I_1 \omega_1^2 \quad \text{and} \quad E_2 = \frac{1}{2} I_2 \omega_2^2 \]

5. **Substituting Angular Velocities**:
- Substitute \( \omega_1 \) and \( \omega_2 \) into the kinetic energy equations:
\[ E_1 = \frac{1}{2} I_1 \left(\frac{L}{I_1}\right)^2 = \frac{1}{2} \frac{L^2}{I_1} \]
\[ E_2 = \frac{1}{2} I_2 \left(\frac{L}{I_2}\right)^2 = \frac{1}{2} \frac{L^2}{I_2} \]

6. **Comparing Kinetic Energies**:
- Since \( I_1 > I_2 \), it follows that:
\[ \frac{1}{I_1} < \frac{1}{I_2} \]
- Therefore:
\[ E_1 < E_2 \]
- This implies that the kinetic energy of the second body is greater than that of the first body:
\[ E_2 > E_1 \]

### Conclusion:
Thus, the correct conclusion is that the kinetic energy of the second body is greater than that of the first body, or:
\[ E_2 > E_1 \]