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⚛️ Physics  ·  Gravitation  ·  NEET & JEE

The gravitational potential energy of a 2 kg mass resting on a planet surface is &minus;8 &times; 10<sup>7</sup> J. The escape speed from that surface is about:

Answer: 8.9 km/s.

  • A 4.5 km/s
  • B 6.3 km/s
  • C 12.6 km/s
  • D 8.9 km/s

Correct answer: D. 8.9 km/s

Explanation: |U| = GMm/R, and v<sub>e</sub> = &radic;(2GM/R) = &radic;(2|U|/m) = &radic;(2 &times; 8 &times; 10<sup>7</sup>/2) &asymp; 8.9 km/s.

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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