Question

If $g$ on the surface of the Earth is $9.8m{s}^{-2}$, its value at a height of $6400km$ is: (Radius of the Earth $=6400km$)

• A. $4.9m{s}^{-2}$
• B. $9.8m{s}^{-2}$
• C. $2.45m{s}^{-2}$
• D. $19.6m{s}^{-2}$

Answer 1

Answer: (C)

$2.45m{s}^{-2}$

The expression for $g$ is given by:
$g_R=\frac{GM}{R^2}$
The value of $g$ changes according to
$g_h=\frac{GM}{(R+h{)}^2}$
Therefore, $\frac{g_h}{g_R}=\frac{R^2}{(R+h{)}^2}$
Here, $h=R$
So, $\frac{g_h}{g_R}=(\frac{R}{R+h}{)}^2$
$\Rightarrow \frac{g_h}{g_R}=(\frac{R}{R+R}{)}^2$
$\Rightarrow g_h=g_R\times \frac{1}{4}=9.8\times 0.25=2.45m/s^2$