Question

Which of the following statement(s) is/are incorrect?

• A. Acceleration due to gravity decreases with altitude.
• B. Acceleration due to gravity increases with increasing depth (assume the earth to be a sphere of uniform density).
• C. Acceleration due to gravity increases with latitude.
• D. Acceleration due to gravity is independent of the mass of the object.

Answer 1

Answer: (B)

Acceleration due to gravity at altitude $h$,
$g_h=\frac{g}{(1+h/R{)}^2}\approx g\left(1-\frac{2h}{R}\right)$
At depth $d,g_d=g\left(1-\frac{d}{R}\right)$
In both cases with increase in $h$ and $d,g$ decreases.
$\Lambda t$ latitude $\psi ,g_{\varphi }-g-{\omega }^{2}R{\cos }^2\psi$
As $\varphi$ increases, $g_{\varphi }$ increases.
Also, we can conclude from the formulae, that it is independent of mass.