Given below are two statements:
Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g)
Statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at the pole is maximum.
In the light of the above statements, choose the correct answer from the options given below

Solution

Physics sir · 4 steps

Do not mix up where g is largest with where rotation matters most: they are opposite places.

1. Why rotation matters. A body on the rotating earth moves in a circle about the axis of rotation. Part of gravity is used up to supply the centripetal force, so the effective g comes out smaller.

   g' = g - ω² R cos² λ

2. Check both ends. At the equator λ = 0°, so cos² λ = 1 and the reduction is the largest possible, ω² R ≈ 0.034 m s⁻². At the pole λ = 90°, so cos² λ = 0 and rotation has no effect at all, because the body sits on the axis and does not go round in a circle.
3. Judge the statements. Statement I is true: rotation does change g. Statement II is false: it has the two ends the wrong way round. The effect is maximum at the equator and zero, its minimum, at the pole.
4. So. Statement I is true and Statement II is false, which is option (b).

The idea to keep. Rotation reduces g by ω² R cos² λ. The effect is biggest at the equator and zero at the poles, which is why g itself is smallest at the equator and largest at the poles.

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