Which of the following options are correct ?

Options

A. Acceleration due to gravity decreases with increasing 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 increasing latitude.
D. Acceleration due to gravity is independent of mass of the earth.

Answer

A, C

Explanation

At altitude `h`, `g_(h) = (gR^(2))/((R + h)^(2)) = (g)/((1 + h//R)^(2))`
As `h` increases, `g_(h)` decreases.
At depth `d`, `g_(d) = g (1- (d)/(R ))`, As `d` increases, `g_(d)` decreases
At latitude `lambda`, `g_(lambda) = g - R omega^(2) cos^(2) lambda`, As `lambda` increases, the value of `cos lambda` decresas so `g_(lambda)` increases
On surface of earth, `g = (GM)/(R^(2))`, i.e., `g` depends on mass `M` of the earth.