Question

explain the variation of the value of g

Answer 1

there are three reasons for the change in value of g

1.shape of the earth

the earth is not exactly spherical .it bulges at the equator and flat at the poles .so the value of g is larger at the poles and smaller at the equator

2. chamge in height

as we go above the surface of the earth the distance of the object increases at the value of g decreases

3 change in depth

the radius of the earth decreases and the g increases

follow..

Answer 2

Variation of Acceleration due to gravity with height

At a height of h from the surface of the earth, the gravitational force on an object of mass m is

F = GMm/(R+h)^2

Here (R + h) is the distance between the object and the centre of earth.

Say at that height h, the gravitational acceleration is g1.

So we can write, mg1 = GMm / (R+h)^2

=> g1 = GM/(R+h)^2 _________________ (5)

Now we know on the surface of earth, it is

g = GM / R^2

Taking ratio of these 2,

g1/g = R^2 /(R+h)^2

= 1/(1 + h/R)^2 = (1 + h/R)^(-2) = (1 – 2h/R)

=> g1/g = (1 – 2h/R)

=> g1 = g (1 – 2h/R) ___________________ (6)

So as altitude h increases, the value of acceleration due to gravity falls.

Variation of Acceleration due to Gravity with depth