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JEE Main20205 Sep 2020Morning ShiftPhysicsGravitationActual

The value of the acceleration due to gravity is g 1 at a height h = R 2 ( R = radius of the earth) from the surface of the earth. It is again equal to g 1 at a depth d below the surface the earth. The ratio d R equals:

Options

  1. A4 9
  2. B5 9
  3. C1 3
  4. D7 9

Correct answer

B. 5 9

Step-by-step solution

Given that g n = g d G M ( R + h ) 2 = G M R 3 ( R - d ) G M ( R + R / 2 ) 2 = G M R 3 ( R - d ) 4 G M 9 R 2 = G M R 2 1 - d R 4 9 = 1 - d R d R = 1 - 4 9 = 5 9 d = 5 9 R

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