Question

derive an expression for variation in gravitational acceleration of the earth at which latitude​

Answer 1

Answer:

This is an expression for acceleration due to gravity at a point P on the surface of the earth having latitude 'Φ'. At the equator Φ = 0°. Hence 'g' is the minimum on the equator.

Answer 2

Variation in gravitation acceleration is $g_{\phi} = g - Rw^{2} Cos^{2} \phi$ of the earth to the latitude.

Explanation:

The particular point at latitude is under the influence of centrifugal force. So, centrifugal force at that point is $mw^{2} r$ .

Taking outward component of this force, which is,

                            = $mw^{2} r Cos\phi$

where, 'Ф' is the angle between the equater and the line joining that point at latitude and centre of earth.

force of gravity is 'mg'.

effective force at that point is

                             = mg - mw^{2} r$Cos\phi$

Consider,

                           ⇒ $mg_{\phi}$ = effective force

                            ⇒ $mg_{\phi} = mg - mw^{2} r Cos\phi$

                            ⇒ $g_{\phi} = g - w^{2} r Cos\phi$    .......   (1)

According to figure,

                                r = R CosФ

where, r is distance of vertical axis to latitude point.

put above equation in (1),

                             ⇒ $g_{\phi} = g - w^{2} R$

Required Answer.