Question

What will be the acceleration due to gravity at a depth d, where g is acceleration due to gravity on the surface of earth?

• A. $\frac{g}{\left[1+\frac{d}{R}\right]^{2}}$
• B. $g\left[1-\frac{2 h}{R}\right]$
• C. $\frac{g}{\left[1-\frac{d}{R}\right]^{2}}$
• D. $g\left[1-\frac{d}{R}\right]$

Answer 1

Answer: (D)

$g =\frac{4}{3} \pi \rho GR$ at earth surface
$g=\frac{4}{3} \pi \rho G(R-d)$ at depth $d$ of earth
$g=g\left[1-\frac{d}{R}\right]$