Question

Which of the following statements is correct?

• A. Acceleration due to gravity increases with increasing altitude
• B. Acceleration due to gravity increases with increasing depth
• C. Acceleration due to gravity increases with increasing latitude
• D. Acceleration due to gravity is independent of the mass of the earth

Answer 1

Answer: (C)

Acceleration due to gravity at a altitude $h$ above the earths surface is
$g_h=\frac{g{R}_E^2}{{\left(R_E+h\right)}^2}\dots \left(i\right)$
where $g$ is the acceleration due to gravity on the earths surface and $R_E$ is the radius of the earth.
$Eq.(i)$ shows that acceleration due to gravity decreases with increasing altitude.
Acceleration due to gravity at a depth d below the earths surface is
$g_d=g\left(1-\frac{d}{R_E}\right)\dots \left(ii\right)$
$Eq.(ii)$ shows that acceleration due to gravity decreases with increasing depth.
Acceleration due to gravity at latitude $\lambda$
$g_{\lambda }=g-R_E{\omega }^{2}co{s}^2\lambda \dots \left(ii\right)$
where $\omega$ is the angular speed of rotation of the earth.
$Eq.(iii)$ shows that acceleration due to gravity increases with increasing latitude.
Acceleration due to gravity of body of mass $m$ is placed on the earths surface is
$g=\frac{G{M}_E}{R_E^2}\dots \left(iv\right)$
$Eq.(iv)$ shows that acceleration due to gravity is independent of the mass of the body but it depends upon the mass of the earth.