Question

A body is taken to a height of $nR$ from the surface of the earth. The ratio of the acceleration due to gravity on the surface to that at the altitude is

• A. $(n+1{)}^2$
• B. $(n+1{)}^{-2}$
• C. $(n+1{)}^{-1}$
• D. $(n+1)$

Answer 1

Answer: (A)

$(n+1{)}^2$

Acceleration due to gravity at the surface of the earth=$g=\frac{GM}{R^2}$

where $R$ is the radius of earth.

Acceleration due to gravity at height $nR=g^{\prime }=\frac{GM}{(R+nR{)}^2}=\frac{GM}{R^2}\frac{1}{(n+1{)}^2}$

$⟹\frac{g}{g^{\prime }}=(n+1{)}^2$