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⚛️ Physics  ·  Gravitation  ·  NEET & JEE

A planet is at perihelion (closest) and aphelion (farthest). Speed ratio v<sub>perihelion</sub> : v<sub>aphelion</sub> equals:

Answer: r aph : r per.

  • A r<sub>aph</sub> : r<sub>per</sub>
  • B r<sub>per</sub> : r<sub>aph</sub>
  • C r<sub>aph</sub><sup>2</sup> : r<sub>per</sub><sup>2</sup>
  • D r<sub>per</sub><sup>2</sup> : r<sub>aph</sub><sup>2</sup>

Correct answer: A. r<sub>aph</sub> : r<sub>per</sub>

Explanation: By conservation of angular momentum: m x v<sub>per</sub> x r<sub>per</sub> = m x v<sub>aph</sub> x r<sub>aph</sub>. So v<sub>per</sub>/v<sub>aph</sub> = r<sub>aph</sub>/r<sub>per</sub>.

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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