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99 Percentile Qs Bank for JEE MainPhysicsGravitation

At what depth below surface of the earth, the acceleration due to gravity will be half its value of that at 1600   km above the surface of the earth?

Options

  1. A4 . 8 × 10 6   m
  2. B3 . 19 × 10 6   m
  3. C1 . 59 × 10 6   m
  4. D5 . 5 × 10 6   m

Correct answer

A. 4 . 8 × 10 6   m

Step-by-step solution

Acceleration due to gravity at a height, g h = g 1 - 2 h R ⇒ g h = g 1 - 2 × 1600 × 10 3 6400 × 10 3 ⇒ g h = g 1 - 0 . 5 ⇒ g h = 5   m   s - 2 Given, 2 . 5 = 10 1 - d R ⇒ 1 4 = 1 - h R ⇒ 3 4 = d R ⇒ d = 3 4 × 6400 × 10 3 ⇒ h = 4 . 8 × 10 6   m

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