JEE Physics 2023 Question with Solution

Given: Two statements about acceleration due to gravity on and inside the Earth.

Find: Which statement is true.

On the Earth's surface, effective acceleration due to gravity depends on latitude:

$$g_{\text{eff}} = g - \omega^2 R \sin^2\theta$$

where $\theta$ is the co-latitude angle. Hence, acceleration due to gravity is different at different places on the surface of Earth, so Statement-I is true.

Inside the Earth, acceleration due to gravity at depth $d$ is:

$$g_{\text{eff}} = g \left( 1 - \frac{d}{R} \right)$$

where $d$ is depth. As $d$ increases, the factor $\left(1 - \frac{d}{R}\right)$ decreases, so acceleration due to gravity decreases below the Earth's surface. Therefore, Statement-II is false.

Thus, the correct option is C.

The solution states that:

$$g_{\text{eff}} = g - \omega^2 R_e \sin^2\theta$$

with $\theta$ as co-latitude, showing that gravity varies with position on the Earth's surface.

It also gives:

$$g_{\text{eff}} = g\left(1 - \frac{d}{R}\right)$$

for depth $d$ inside the Earth, which clearly decreases as $d$ increases.

Therefore, Statement I is true but Statement II is false, so the correct option is C.