Question

A particle is taken to a height $R$ above the earth's surface, where $R$ is the radius of earth. The acceleration due to gravity there is

• A. $2.45m/s^2$
• B. $4.9m/s^2$
• C. $9.8m/s^2$
• D. $19.6m/s^2$

Answer 1

The correct option is A $2.45m/s^2$

Let $g$ be the acceleration due to gravity at earth's surface
So,
$g=\frac{GM}{R^2}\to \left(1\right)$

Now let $g^{\prime }$ be the acceleration due to gravity above at a distance $R$ from the earth's surface

so, $g^{\prime }=\frac{GM}{(R+R{)}^2}\to \left(2\right)$

$\Rightarrow \frac{g}{g^{\prime }}=\frac{GM}{R^2}\times \frac{(R+R{)}^2}{GM}$
$\Rightarrow \frac{g}{g^{\prime }}=\frac{(2R{)}^2}{R^2}$
$\Rightarrow \frac{g}{g^{\prime }}=4$
$\Rightarrow g^{\prime }=\frac{g}{4}$

if $g=9.8m/s^2$, then $g^{\prime }=\frac{9.8}{4}m/s^2$
$\Rightarrow g^{\prime }=2.45m/s^2$