JEE Main 2023 — Gravitation Question with Solution

Acceleration due to gravity is the acceleration acquired by a freely falling object.

At any particular place on the Earth, the acceleration due to gravity depends on the latitude of the place and the angular frequency of Earth's rotation. Mathematically, the latitude dependence of acceleration due to gravity can be written as

$g_{\mathrm{eff}}= g-R{\omega }^2{\cos }^2\lambda .................\left(1\right)$

where, $g_{\mathrm{eff}}$ is the effective acceleration due to gravity, $g$ is the real value of gravity at the latitude without considering earth rotation, $R$ is the radius of Earth, $\omega$ is the angular frequency of rotation and $\lambda$ is the latitude of the place.

According to equation (1), the value of the acceleration due to gravity varies from place to place.

The variation of acceleration due to gravity with the depth can be written as

$g_d= g\left(1-\frac{d}{R}\right)....................\left(2\right)$

where, $g_d$ is the acceleration due to gravity at a depth $d$ from the surface and $g$ is the acceleration due to gravity at the surface.

From equation (2), it can be stated that the acceleration due to gravity decreases with the depth.

Hence, Statement I is true, but statement II is false.