Which of the following option 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 the mass of the earth.

Answer

A, C

Explanation

Acceleration due to gravity at a height h above the earth.s surface is
Since, `g_(h) = (g R^(2))/((R+h)^(2))`
`= (g)/(1+(g)/(R )^(2)) ~= g(1-(2h)(R ))`
As h increases, `g_(h)` decreases.
Acceleration due to gravity at a depth d below the earth.s surface is
`g_(d) = g(1-(d)/(R ))`
As d increases, `g_(d)` decreases.
Acceleration due to gravity at a latitude `lambda` is
`g_(lambda) = g - R omega^(2) cos lambda`
As `lambda` increases, `g_(lambda)` increases.
Also, acceleration due to gravity is given by
`g = (GM)/(R^(2))`, i.e., g depends upon M.
`:.` The correct options are (a) and (c ).