JEE Main 2023 — Gravitation Question with Solution

Let's analyze both statements:

Statement I: Rotation of the earth shows an effect on the value of acceleration due to gravity (g).

This is true. The value of $g$ is affected by the rotation of the Earth. The centripetal force due to the Earth's rotation causes a reduction in the perceived gravitational acceleration for objects on the surface. This effect is zero at the poles and increases towards the equator. The formula for the effective acceleration due to gravity at a latitude $\theta$ is:

where:

• $g$ is the theoretical acceleration due to gravity without Earth's rotation,
• $R$ is the radius of the Earth,
• $\omega$ is the angular velocity of the Earth's rotation, and
• $\theta$ is the latitude.

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.

This is false. For clarification, the effect of the Earth's rotation on the value of $g$ is maximum at the equator and minimum at the poles. At the equator, the centrifugal force is highest because of the maximum velocity due to Earth's rotation, which decreases the effect of gravity more than at any other latitude. At the poles, the centrifugal force is zero since there is no rotational velocity contributing to a centripetal effect; therefore, the effect of rotation on $g$ is minimum (zero).

With these considerations, the correct option is:

Option B: Statement I is true but Statement II is false.