Statement-I: If the earth expands in size without any change in mas, the length of the day would increase.
statement-II: The rotation of earth about its axis follows the law of conservation of angular momentum.

Options

A. If both Statement-I and Statement-II are true, and Statement - II is the correct explanation of Statement– I.
B. If both Statement-I and Statement-II are true but Statement - II is not the correct explanation of Statement – I.
C. If Statement-I is true but Statement-II is false.
D. If Statement-I is false but Statement-II is true.

Answer

To solve the question, we need to analyze the two statements provided and determine their validity based on the principles of rotational motion and conservation laws.

### Step-by-Step Solution:

1. **Understanding Statement-I**:
- Statement-I claims that if the Earth expands in size without any change in mass, the length of the day would increase.
- When the Earth expands, its radius (R) increases while its mass (M) remains constant.

2. **Moment of Inertia**:
- The moment of inertia (I) of a solid sphere is given by the formula:
\[ I = \frac{2}{5} M R^2 \]
- Since the mass (M) is constant and the radius (R) is increasing, the moment of inertia (I) will also increase.

3. **Conservation of Angular Momentum**:
- According to the law of conservation of angular momentum, if no external torque acts on a system, the angular momentum (L) remains constant. Angular momentum is given by:
\[ L = I \omega \]
- Here, \( \omega \) is the angular velocity. Since \( L \) is constant and \( I \) is increasing, \( \omega \) must decrease to keep \( L \) constant.

4. **Relating Angular Velocity to Time Period**:
- The time period (T) of rotation is related to angular velocity by the equation:
\[ T = \frac{2\pi}{\omega} \]
- If \( \omega \) decreases, then \( T \) must increase. This means that the length of the day (which is one complete rotation of the Earth) will increase.

5. **Conclusion for Statement-I**:
- Therefore, Statement-I is true: if the Earth expands in size without any change in mass, the length of the day would indeed increase.

6. **Understanding Statement-II**:
- Statement-II states that the rotation of the Earth about its axis follows the law of conservation of angular momentum.
- This is a fundamental principle in physics. Since no external torque is acting on the Earth, its angular momentum is conserved.

7. **Conclusion for Statement-II**:
- Thus, Statement-II is also true.

8. **Final Conclusion**:
- Both statements are true. Therefore, the correct option is that both Statement-I and Statement-II are true.