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⚛️ Physics  ·  Gravitation  ·  NEET & JEE

A planet has the same mean density as another but twice its radius. Its escape velocity, compared with the smaller planet, is:

Answer: it doubles.

  • A it halves
  • B it stays the same
  • C it quadruples
  • D it doubles

Correct answer: D. it doubles

Explanation: v<sub>e</sub> = √(2GM/R) = R√(8πGρ/3), so at constant density v<sub>e</sub> ∝ R. Doubling R doubles the escape velocity.

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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