Question

The acceleration to gravity at a height 1/20th of the radius of the earth above the earth surface is $9m{s}^{-2}$ . Its value at a point at an equal distance below the surface of the earth in $m{s}^{-2}$ is about

• A. 8.5
• B. 9.5
• C. 9.8
• D. 11.5

Answer 1

Answer: (B)

At a height $h$ ,
$g_h=g\left(1-\frac{2h}{R}\right)$
for $h=\frac{R}{20}$ we get
$9=g\left(1-\frac{1}{10}\right)=\frac{9}{10}g$
At a depth $d$ ,
$g_d=g\left(1-\frac{d}{R}\right)$
for $d=\frac{R}{20}$
$g_d=g\left(1-\frac{1}{20}\right)=\frac{19}{20}g$
$\Rightarrow \frac{g_d}{9}=\frac{19}{18}\Rightarrow g_d=9.5m{s}^{-2}$