Assuming the earth to be a sphere of uniform density, its acceleration due to gravity acting on a body:

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1.  **Formula for g:** The acceleration due to gravity on the surface of the Earth is given by $g = \frac{GM_E}{R_E^2}$, where $G$ is the gravitational constant, $M_E$ is the mass of the Earth, and $R_E$ is the radius of the Earth .
2.  **Independence of Body Mass:** The expression for $g$ depends only on the mass and dimensions of the source mass (Earth). It does not contain the term $m$ (mass of the body). Thus, all bodies fall with the same acceleration, regardless of their mass . (Statement 4 is correct).
3.  **Variation with Altitude:** As altitude $h$ increases, the distance $r = R_E + h$ increases. Since $g \propto \frac{1}{r^2}$, $g$ decreases with increasing altitude . (Statement 1 is incorrect).
4.  **Variation with Depth:** Inside the Earth (assumed uniform sphere), $g(d) = g_{surface} (1 - \frac{d}{R_E})$. As depth $d$ increases, $g$ decreases linearly, becoming zero at the center . (Statement 2 is incorrect).
5.  **Dependence on Earth's Mass:** The formula explicitly includes $M_E$. Thus, $g$ depends on the mass of the Earth. (Statement 3 is incorrect).

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