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?

Question

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?, 4 . 8 × 10 6 m, 3 . 19 × 10 6 m, 1 . 59 × 10 6 m, 5 . 5 × 10 6 m

MARKS App · Accepted Answer

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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