Which of the following statements is correct ? .

Options

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

Answer

C

Explanation

Accleration 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_(epsilon)` is the radius of the earth. Eq(i) shows that acceleration due to gravity decreases with increasing altitude. Acceleration due to gravity at a depth h belwo the earth's surface is
`g_(d)=g=(1-d/(R_(E))).......(ii)`
Eq(ii) shows that acceleration due to gravity decreases with increasing depth. Acceleration due to gravity at a latitude `lambda`
`g_(lambda)=g R_(E)omega^(2)cos^(2)lambda`
where `omega` is the angular speed of rotation of the earth.
Eq(iii) shows that acceleration due to gravity increases with increases 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 dependence upon the mass of the earth.