Assertion : If the ice on the polar caps of the earth melts, then length of day will increase.
Reason : Moment of inertia of the earth increases, as ice on polar caps melts.

Options

A. If both the Asseration and Reason are true and reason explains the Assertion :
B. If both the Assertion and Reason are true but reason does ot explain the Assertion :
C. If Assertion is true but reason false
D. If Assertion is false but reason is true

Answer

To solve the problem, we need to analyze the assertion and the reason provided in the question step by step.

### Step 1: Understanding the Assertion
The assertion states that if the ice on the polar caps of the Earth melts, then the length of the day will increase. This suggests that the time it takes for the Earth to complete one rotation (one day) will become longer.

**Hint:** Consider how the melting of ice affects the distribution of mass on Earth.

### Step 2: Understanding the Reason
The reason given is that the moment of inertia of the Earth increases as the ice on the polar caps melts. Moment of inertia (I) is a measure of an object's resistance to changes in its rotation. When ice melts, it moves from a position near the axis of rotation (the poles) to a position further away from the axis (the equator), increasing the moment of inertia.

**Hint:** Recall the formula for moment of inertia and how it depends on the distribution of mass relative to the axis of rotation.

### Step 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) of the system remains constant. The angular momentum is given by the product of the moment of inertia and angular velocity (ω):
\[ L = I \cdot \omega \]

When the ice melts, the moment of inertia increases (I increases), and since angular momentum must remain constant, the angular velocity (ω) must decrease. This means that the Earth will rotate more slowly, leading to an increase in the time taken for one complete rotation (length of the day).

**Hint:** Think about how changes in moment of inertia affect angular velocity when angular momentum is conserved.

### Step 4: Relating Moment of Inertia to Length of Day
From the relationship \( L = I \cdot \omega \), we can express this in terms of the time period (T) for one complete rotation:
\[ T = \frac{2\pi I}{L} \]
If I increases (due to the melting ice), T must also increase to keep L constant. Therefore, the length of the day (T) increases.

**Hint:** Consider how the relationship between moment of inertia and time period leads to the conclusion about the length of the day.

### Conclusion
Both the assertion and the reason are true. The melting of polar ice increases the moment of inertia of the Earth, which in turn causes the length of the day to increase due to the conservation of angular momentum.

### Final Answer
- Assertion: True
- Reason: True
- The reason is the correct explanation for the assertion.