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

Answer 1

Answer: (D)

$g{\left[1-\frac{d}{R}\right]}$

Answer 2

Acceleration due to gravity at the surface of the earth $g=\frac{GM}{R^2}=\frac{4}{3}\pi \rho GR$ ...(i) Acceleration due to gravity at depth d from the surface of earth $g'=\frac{4}{3}\pi \rho \pi G(R - d)$ ....(ii) From Eqs. (i) and (ii) $g'=g\left[1-\frac{d}{R}\right]$