At a certain depth d below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height 3 R above earth surface. Where R is Radius of earth (Take R = 6400 km ). The depth d is equal to

Step-by-step solution

The magnitude of acceleration due to gravity g 1 at a depth of d below the surface of Earth is g 1 = G M R 3 R - d = G M R 2 1 - d R ....(1) The magnitude of acceleration due to gravity g 2 at a height d above the surface of Earth is g 2 = G M R + d 2 ....(2) Given here, g 1 = 4 g 2 G M R 2 1 - d R = 4 G M R + 3 R 2 ⇒ G M R 2 1 - d R = 4 G M 4 R 2 ⇒ 1 - d R = 1 4 ⇒ d R = 3 4 ⇒ d = 3 4 R ⇒ d = 4800   km