At what altitude will the acceleration due to gravity be 25 % of that at the earth's surface (given radius of the earth is R )

Question

At what altitude will the acceleration due to gravity be 25 % of that at the earth's surface (given radius of the earth is R ), R 4, R, 3 R 8, R 2

MARKS App · Accepted Answer

g = GM r 2 ⇒ g 0 = GM R 2 . . . ( 1 ) ⇒g h = GM R + h 2 . . . ( 2 ) g h g 0 = R R + h 2 ⇒ 1 4 = R R + h 2 ⇒ R R + h = 1 2 ⇒R + h = 2 R ⇒ h = R