Question

If R is the radius of the earth, then the ratio of acceleration due to gravity on surface of the earth to acceleration due to gravity at height nR is:

• A. ${\left(n+1\right)}^{-1}$
• B. ${\left(n+1\right)}^2$
• C. ${\left(n+1\right)}^{-2}$
• D. ${\left(n+1\right)}^3$

Answer 1

The correct option is B ${\left(n+1\right)}^2$

Given

Radius of Earth$=R$

Acceleration due to gravity $g=\frac{GM}{R}$

Also

$g^{\prime }=g\left(\frac{1-2h}{R}\right)$

Given height $=nR$

$g^{\prime }=g\left(\frac{1-2nR}{R}\right)$

When body is raised by $nR$

$g^{\prime }=\frac{GM}{(R+nR{)}^2}{g}^{\prime }=\frac{GM}{R(1+n{)}^2}$

Now ratio of $g$ and $g^{\prime }$

$\Rightarrow (n+1{)}^2$