Question

Acceleration due to gravity is $g$ on the surface of the earth. Then, the value of the acceleration due to gravity at a height of $32km$ above earth's surface is (assume radius of earth to be $6400km$)

• A. $0.99gm{s}^{-2}$
• B. $0.8gm{s}^{-2}$
• C. $1.01gm{s}^{-2}$
• D. $0.9gm{s}^{-2}$

Answer 1

The correct option is A

$0.99gm{s}^{-2}$

Step 1. Given data

Height above the earth's surface, $h=32km$

The radius of the earth, $R_e=6400km$

Step 2. The explanation for the correct option:

For the height,$h$ above the earth’s surface,

$\begin{array}{l}g’=g\left(1-\frac{2h}{R_e}\right)\end{array}$

Where, $g^{\text{'}}$is the acceleration due to gravity at height $h$

$R_e$ is the radius of the earth

$g$ is the acceleration due to gravity on the surface of the earth

$\begin{array}{l}g’=g(1-\frac{64}{6400})\\ =g(1-0.01)\\ =0.99gm{s}^{-2}\end{array}$

Hence, option $\left(A\right)$ is correct.