Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude.
Reason R: At equator, the direction of acceleration due to the gravity is towards the center of earth.
In the light of above statements, choose the correct answer from the options given below

Let us analyze both the Assertion and Reason carefully.

Assertion A: "If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude."

Analysis of Assertion A:

The effective gravitational acceleration at a latitude $$\lambda$$ on the rotating Earth is:

$$g_{eff} = g - R\omega^2\cos^2\lambda$$

where $$g$$ is the gravitational acceleration without rotation, $$R$$ is the radius of the Earth, and $$\omega$$ is the angular velocity of Earth's rotation.

Variation in magnitude: At the poles ($$\lambda = 90°$$), $$g_{eff} = g$$. At the equator ($$\lambda = 0°$$), $$g_{eff} = g - R\omega^2$$, which is smaller. So the magnitude clearly varies as we move from poles to equator. This part of the assertion is false.

Variation in direction: The centrifugal acceleration at latitude $$\lambda$$ is directed perpendicular to Earth's rotation axis (i.e., radially outward from the axis, not from the center of Earth). Only at the equator and at the poles does the centrifugal acceleration align radially with respect to Earth's center. At intermediate latitudes, the centrifugal force has a component tangential to the Earth's surface, causing the net effective gravity to deviate slightly from pointing towards the center. So the direction also varies, making the assertion false.

Reason R: "At the equator, the direction of acceleration due to gravity is towards the center of earth."

Analysis of Reason R:

At the equator, the centrifugal acceleration $$R\omega^2$$ is directed radially outward from Earth's center (since at the equator, the direction perpendicular to the rotation axis coincides with the radial direction from Earth's center). The gravitational pull is directed radially inward towards the center. Since both are along the same line (radial direction), the resultant effective gravity still points towards the center of Earth. Only the magnitude is reduced. This makes Reason R true.

Conclusion:

The Assertion is false (both magnitude and direction vary) but the Reason is true (at the equator specifically, the direction is towards the center).

Hence, the correct answer is Option D.