Which of the following statement is correct ?

Options

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

Answer

C

Explanation

(c ) Acceleration due to gravity at a altitude h above the earth's surface is
`g_(h)=(gR_(E)^(2))/((R_(E)+h)^(2))` …..(i)
where g is the acceleration due to gravity on the earth's surface and `R_(E)` is the radius of the earth.
Eq.(i) shows that acceleration due to gravity decrease with increasing altitude.
Acceleration due to gravity at a depth d below the earth's surface is
`g_(d)=g(1-(d)/(R_(E)))`....(ii)
Eq. (ii) shows that acceleration due to gravity decrease with increasing depth.
Acceleration due to gravity at latitude `lambda`
`g_(lambda)=g-R_(E)omega^(2) cos^(2)lambda`........(iii)
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 earth's surface is
`g=(GM_(E))/(R_(E)^(2))`.......(iv)
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.