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 3R above earth surface, where R is radius of earth. [Take R = 6400 km] The depth d is equal to:
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Question

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 3R above earth surface, where R is radius of earth. [Take R = 6400 km] The depth d is equal to:

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G1 Physics · Accepted Answer

At height 3R, distance from centre is 4R, so g(h)=g/16. Four times this is g/4. Inside Earth, g(d)=g(1−d/R). Thus 1−d/R = 1/4, giving d = 3R/4 = 4800 km.