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JEE Main202131 Aug 2021Evening ShiftPhysicsGravitationActual

If R E be the radius of Earth, then the ratio between the acceleration due to gravity at a depth r below and a height r above the earth surface is: (Given : r < R E )

Options

  1. A1 + r R E - r 2 R E 2 - r 3 R E 3
  2. B1 + r R E + r 2 R E 2 + r 3 R E 3
  3. C1 - r R E - r 2 R E 2 - r 3 R E 3
  4. D1 + r R E - r 2 R E 2 + r 3 R E 3

Correct answer

A. 1 + r R E - r 2 R E 2 - r 3 R E 3

Step-by-step solution

g h g d = G M R E + r 2 G M R E 3 R E - r = R E 3 R E + r 2 R E - r g d g h = R E + r 2 R E - r R E 3 = R E 3 - R E r 2 + r R E 2 - r 3 R E 3 = 1 - r 2 R E 2 + r R E - r R E 3

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