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⚛️ Physics  ·  Gravitation  ·  NEET & JEE

The acceleration due to gravity at a depth equal to half the Earth radius (compared with the surface value g) is:

Answer: g/2.

  • A g/2
  • B g/4
  • C 2g
  • D g

Correct answer: A. g/2

Explanation: g' = g(1 − d/R) = g(1 − 1/2) = g/2.

Variation of g with Height and Depthgg_surfaceAbove surface: g ∝ 1/r² (falls off curving down)Below surface: g ∝ r (falls off LINEARLY)Earth's surface (r = R)centre (r=0): g=0g is MAXIMUM exactly at the surface - it decreases in both directions, but by different laws

g is maximum at Earth's surface; going up, it falls off as 1/r² (inverse-square); going down, it falls off linearly with depth (since only the mass enclosed within radius r contributes), reaching zero at the centre.

Concept context

Universal gravitation, orbital mechanics, gravitational potential, and escape velocity.

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