Given below are two statements :
Statement-I: Acceleration due to gravity is different at different places on the surface of earth.
Statement-II: Acceleration due to gravity increases as we go down below the earth's surface.
In the light of the above statements, choose the correct answer from the options given below

We need to evaluate two statements about acceleration due to gravity.

The first statement is "Acceleration due to gravity is different at different places on the surface of earth." This statement is true because the acceleration due to gravity $$g$$ on Earth's surface varies for several reasons.

Since Earth is an oblate spheroid (flattened at the poles and bulging at the equator) and $$g = \frac{GM}{R^2}$$, the smaller radius $$R$$ at the poles produces a larger value of $$g$$ (approximately $$9.83 \, \text{m/s}^2$$) compared to the equator (approximately $$9.78 \, \text{m/s}^2$$).

Furthermore, Earth's rotation gives rise to a centrifugal effect that reduces the effective acceleration due to gravity. At latitude $$\lambda$$, the effective gravity is given by $$g' = g - R\omega^2\cos^2\lambda$$, which is maximal at the equator (where $$\lambda = 0$$) and zero at the poles (where $$\lambda = 90°$$).

In addition, local variations in Earth's density and differences in altitude also lead to slight changes in the value of $$g$$ from one location to another.

The second statement is "Acceleration due to gravity increases as we go down below the earth's surface." This statement is false.

Under the assumption of uniform density, the acceleration due to gravity at a depth $$d$$ below the surface is given by $$g' = g\left(1 - \frac{d}{R}\right)$$, which shows that $$g'$$ decreases linearly as the depth $$d$$ increases. In particular, at the center of the Earth (where $$d = R$$), $$g' = 0$$ because only the mass within the sphere of radius $$(R - d)$$ contributes to the gravitational pull according to the shell theorem, and this inner mass diminishes with increasing depth.

Statement I is true but Statement II is false.

The correct answer is Option (3): Statement I is true but Statement II is false.