If the earth loses its atmosphere sudenly, then the duration of day will :-

Options

A. increase
B. decrease
C. remain unchanged
D. nothing can be definitely said

Answer

To solve the question of how the duration of a day would change if the Earth suddenly loses its atmosphere, we can break it down into the following steps:

### Step-by-Step Solution:

1. **Understanding the Earth’s Rotation**:
- The Earth rotates around its axis, and this rotation defines the duration of a day. The rotation occurs at a certain angular velocity.

2. **Effect of Atmosphere on Earth's Radius**:
- The atmosphere adds to the effective radius of the Earth. When considering the rotation, the radius \( R \) includes the radius of the Earth plus the thickness of the atmosphere.

3. **Moment of Inertia**:
- The moment of inertia \( I \) of a rotating body is given by the formula \( I = m \cdot r^2 \), where \( m \) is the mass and \( r \) is the radius from the axis of rotation.
- Since the atmosphere contributes to the total mass and radius, its removal will affect the moment of inertia.

4. **Impact of Removing the Atmosphere**:
- If the atmosphere is suddenly removed, the effective radius \( r \) of the Earth decreases. This leads to a decrease in the moment of inertia \( I \).
- A decrease in the moment of inertia while the angular momentum \( L \) (which is conserved) remains constant implies that the angular velocity \( \omega \) must increase, as given by the relationship \( L = I \cdot \omega \).

5. **Conclusion on Duration of Day**:
- Since the angular velocity \( \omega \) increases, the duration of a day (which is inversely proportional to angular velocity) will decrease.
- Therefore, if the Earth loses its atmosphere suddenly, the duration of the day will decrease.

### Final Answer:
The duration of the day will **decrease**.

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