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KVPY2020PhysicsGravitation

At a height of 10   km above the surface of earth, the value of acceleration due to gravity is the same as that of a particular depth below the surface of earth. Assuming uniform mass density of the earth, the depth is,

Options

  1. A1   km
  2. B5   km
  3. C10   km
  4. D20   km

Correct answer

D. 20   km

Step-by-step solution

At a height h g h = g 0 1 - 2 h R when h ( 10   km ) < R ( 6400   km ) at a depth d g d = g 0 1 - d R here g 0 = G M R 2 Now g h = g d ⇒ d = 2 h d = 20   km

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