The value of acceleration due to gravity $10\ km$ below the surface of the earth is ___$m/s^2$?
Radi

Question

The value of acceleration due to gravity $10\ km$ below the surface of the earth is ___$m/s^2$?
Radius of earth = $6400\ km$ and the value of g at the surface of the earth is $9.80 m/s^2$.

Professor PC Thomas Classes · Answer

The value at a depth $h$ is
$
\begin{aligned}
g & =g_0\left(1-\frac{h}{R}ight) \
& =\left(9 \cdot 8 \mathrm{~m} \mathrm{~s}^{-2}ight)\left(1-\frac{10 \cdot 0 \mathrm{~km}}{6400 \mathrm{~km}}ight) \
& =9 \cdot 78 \mathrm{~m} \mathrm{~s}^{-2} .
\end{aligned}
$