Assertion (A): At pole value of acceleration due to gravity (g) is greater than that of equator.
Reason (R) : Earth rotates on its axis in addition to revolving round the sun.

Options

A. If both A and R are true and R is the correct explanation of A.
B. If both A and R are true but R is not the correct explanation of A.
C. If A is true but R is false
D. If A is false but R is true.

Explanation

To solve the problem, we need to analyze the assertion and reason provided.

### Step 1: Understand the Assertion
The assertion states that the value of acceleration due to gravity (g) at the poles is greater than that at the equator. This is a true statement based on the physics of gravity and the Earth's rotation.

### Step 2: Understand the Reason
The reason given is that the Earth rotates on its axis in addition to revolving around the sun. This is also true. The rotation of the Earth affects the value of g experienced at different latitudes.

### Step 3: Analyze the Effect of Earth's Rotation
The effective acceleration due to gravity (g') at any point on the Earth's surface can be expressed as:
\[ g' = g - \omega^2 r \cos^2(\lambda) \]
where:
- \( g \) is the standard acceleration due to gravity (approximately 9.8 m/s²),
- \( \omega \) is the angular velocity of the Earth's rotation,
- \( r \) is the radius of the Earth,
- \( \lambda \) is the latitude.

### Step 4: Calculate g' at the Equator
At the equator, the latitude \( \lambda = 0 \):
\[ g'_{equator} = g - \omega^2 r \cos^2(0) \]
Since \( \cos(0) = 1 \):
\[ g'_{equator} = g - \omega^2 r \]
This shows that the effective gravity at the equator is reduced due to the centrifugal effect of Earth's rotation.

### Step 5: Calculate g' at the Pole
At the poles, the latitude \( \lambda = 90^\circ \):
\[ g'_{pole} = g - \omega^2 r \cos^2(90^\circ) \]
Since \( \cos(90^\circ) = 0 \):
\[ g'_{pole} = g \]
This means that there is no reduction in the effective gravity at the poles due to rotation.

### Step 6: Compare g' at the Equator and the Pole
From the calculations:
- \( g'_{equator} = g - \omega^2 r \) (which is less than g)
- \( g'_{pole} = g \)

Thus, we can conclude that:
\[ g'_{pole} > g'_{equator} \]
This confirms the assertion that the acceleration due to gravity is greater at the poles than at the equator.

### Conclusion
Both the assertion (A) and the reason (R) are true, and the reason correctly explains the assertion.

### Final Answer
Both A and R are true, and R is the correct explanation of A.

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