Question

If $g$ is the acceleration due to gravity on the surface of the earth, its value at a height equal to double the radius of the earth is

• A. $g$
• B. $\frac{g}{2}$
• C. $\frac{g}{3}$
• D. $\frac{g}{9}$

Answer 1

The correct option is D

$\frac{g}{9}$

Step 1: Given data

Acceleration due to gravity $=g$

Height, $h=2R$

We have to find acceleration due to gravity at a height $h$

Step 2: Formula and solution

We know acceleration due to gravity of earth at a height $h$ from the surface of earth is given by,

$g\text{'}=\frac{g}{{\left[1+{\displaystyle \frac{h}{R}}\right]}^2}$

Here, since it is given $h=2R$

$$\begin{gathered} g\text{'}=\frac{g}{{\left[1+{\displaystyle \frac{h}{R}}\right]}^2} \\ \Rightarrow g\text{'}=\frac{g}{{\left[1+{\displaystyle \frac{2R}{R}}\right]}^2} \\ \Rightarrow g\text{'}=\frac{g}{{\left[1+{\displaystyle 2}\right]}^2} \\ \Rightarrow g\text{'}=\frac{g}{9} \end{gathered}$$

Therefore, acceleration due to gravity of earth on an object at a height $h=2R$ is $\frac{g}{9}$

Hence, option D is the correct answer.