# Which of the following options are correct?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.

When a particle is placed on the surface of the earth, then the acceleration due to gravity is given by

…(i)

Now when the particle is at a height h form the surface then new acceleration becomes

…..(ii)

From eqn. (i) and (ii)

Therefore, acceleration due to gravity decreases with increasing altitude

Now, if a body of mass m is placed on the point whose angle of latitude is ϕ then acceleration due to gravity is given by

Where,

ω = angular velocity of earth

As the latitude increases, ϕ increases and cosϕ decreases, thus increasing the value of g

Therefore, (a) and (c) are correct option

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