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⚛️ Physics  ·  Gravitation  ·  NEET & JEE

Two planets have time periods in ratio 8:1. Ratio of orbital radii:

Answer: 4:1.

  • A 2:1
  • B 4:1
  • C 8:1
  • D 16:1

Correct answer: B. 4:1

Explanation: T<sup>2</sup> proportional to r<sup>3</sup> (Kepler). (T<sub>1</sub>/T<sub>2</sub>)<sup>2</sup> = (r<sub>1</sub>/r<sub>2</sub>)<sup>3.</sup> (8)<sup>2</sup> = (r<sub>1</sub>/r<sub>2</sub>)<sup>3.</sup> 64 = (r<sub>1</sub>/r<sub>2</sub>)<sup>3.</sup> r<sub>1</sub>/r<sub>2</sub> = 4.

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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