Question

The height at which the acceleration due to gravity becomes g/9 ( where , g is the acceleration due to gravity on the surface of the earth ) in terms of R , the radius of the earth is [AIEEE 2009]​

Answer 1

Explanation:- As value of acceleration due to gravity above the earth surface is g .

g' = GM/(R+h)² , acceleration due to gravity at height h

But , g' = g/9

we can rewrite as g' = g/9 = GM /R² × R²(R+h)²

• ∵ g= GM/R²

• ∴ g/9 = g× (R/R+h)²

• ⟹ 1/9 = (R/R+h)²
• ⟹ R/R+h = 1/3
• ⟹ 3R= R+ h
• ⟹2R = h

Hence, the radius of the earth is 2R Answer