Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

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

increases with increasing altitude.

increases with increasing depth.

is independent of the mass of the earth.

is independent of the mass of the body.

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 .
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).
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).
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).
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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