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Variation in the values of ‘g’ on the surface of earth is due to the following reasons
(a) Due to shape of earth: An structure of earth the gravity is given by . The earth is elliptical in shape. It is flatter at the poles and bulged out at the equator. Now, as , therefore the value of g at the equator is minimum and the value of g at the poles is maximum ( Radius at poles is < Radius at equator).
(b) Due to rotation of earth : Earth rotates about its axis therefore every object placed on the surface of earth also rotates about the same axis. If the observed value of g at the latitude l is represented by gl, then
where w is the angular velocity of rotation of the earth.
At equator l = 0º and hence cos l = 1 (minimum value of gravity)
At poles (maximum values gravity)
Variation of ‘g’ above the surface of earth: As we go above the surface of the earth, the value of ‘g’ decreases
(i) Consider a body of mass m at a height ‘h’ above the surface of earth. (Let Re is the radius of earth and Me is the mass of earth) if h << Re, then expanding binomially and neglecting higher power of h/Re, we get
or gn = (where )
So near the surface of earth gravity varies linearly with height
Variation of ‘g’ below the surface of earth: The value of ‘g’ decreases as we go below the surface of earth because the effective mass of earth attracting the body decreases.
The value of ‘g’ at a depth x from the surface of earth is = g - Dg = g - gx/R
At the centre of earth x = R hence g = 0
The decrease in the value of ‘g’ at a depth ‘x’ below the surface of earth is Dg = (gx/R)
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