The height at which the acceleration due to gravity becomes 9 g (where g = the acceleration due to gravity on the surface of the earth) in terms of R , the radius of the earth is

Question

The height at which the acceleration due to gravity becomes 9 g ​ (where g = the acceleration due to gravity on the surface of the earth) in terms of R , the radius of the earth is

TestHub · Accepted Answer

g ′ = ( R + h ) 2 GM ​ , acceleration due to gravity at height h ​ ⇒ 9 g ​ = R 2 GM ​ ⋅ ( R + h ) 2 R 2 ​ = g ( R + h R ​ ) 2 ⇒ 9 1 ​ = ( R + h R ​ ) 2 ⇒ R + h R ​ = 3 1 ​ ⇒ 3 R = R + h ⇒ 2 R = h ​

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