Given below are two statements:
Statement I: Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface.
Statement II: Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's surface, if $$h = d$$.
In the light of above statements, choose the most appropriate answer form the options given below

Statement I: Acceleration due to gravity decreases as you go 'up' or 'down' from earth's surface.

Above the surface: $$g_h = g\left(\frac{R}{R+h}\right)^2$$ which decreases with height $$h$$.

Below the surface: $$g_d = g\left(1 - \frac{d}{R}\right)$$ which decreases with depth $$d$$.

So Statement I is correct.

Statement II: Acceleration due to gravity is same at height $$h$$ and depth $$d$$ if $$h = d$$.

At height $$h$$: $$g_h = g\left(1 - \frac{2h}{R}\right)$$ (for small $$h$$)

At depth $$d$$: $$g_d = g\left(1 - \frac{d}{R}\right)$$

For $$g_h = g_d$$: $$1 - \frac{2h}{R} = 1 - \frac{d}{R}$$, which gives $$d = 2h$$.

So $$g$$ is the same when $$d = 2h$$, not when $$h = d$$. Statement II is incorrect.

The correct answer is Option 3: Statement I is correct but Statement II is incorrect.