Which one of the following option is wrong?

Options

A. Acceleration due to gravity decreases with incresing altitude
B. Acceleration due to gravity decreases 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

D

Explanation

(a) The value of g decreases with increaseing altitude.
`g'=(g)/((1+(h)/(R ))^(2))`
(b) g decreases with increasing depth
`g_(d)=g(1-(d)/(R ))`
Thus (b) is wrong.
(c ) As the latitude `lambda` increases, g' increases.
`g_(lambda)=g-omega^(2)R cos^(2)lambda`
As we go from the equator `(lambda = 0)` to the pole `(lambda = 90^(@))`, g' increases from `g-Romega^(2)` to g. (c ) is correct.
(d) All the formulae do not contain the mass of the earth. Thus (d) is correct.