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:

Solution

Physics sir · 4 steps

Earth spins, so add the centrifugal term: it shrinks g at the equator and tilts it in between.

1. Rotation matters. On the rotating Earth, a body at latitude λ moves in a circle of radius R cos λ about the axis. So the effective g is true gravity combined with a centrifugal term ω² R cos λ that points away from the axis.

   g' = g - ω² R cos² λ

2. Magnitude changes. At the poles λ = 90°, so g' = g. At the equator λ = 0, so g' = g - ω² R, smaller by about 0.034 m s⁻². The magnitude does vary from poles to equator.
3. Direction changes. At the poles the centrifugal term is zero. At the equator it acts along the radius, outward. In both places g' points to the centre. At any latitude in between, the centrifugal term has a sideways part, so g' tilts slightly away from the centre.
4. So. A is false, because both the magnitude and the direction of g change. R is true, because at the equator g' still points to the centre. The answer is (d).

The idea to keep. Effective g is g - ω² R cos² λ. It is least at the equator and greatest at the poles. It points exactly at the centre only at the poles and the equator.

Answer from the NTA final answer key. Solution by PrepWiser.