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pls derive G=g-w2.R.cosx with every explanation plsssss!!!!!!

pls derive G=g-w2.R.cosx
with every explanation plsssss!!!!!!

Grade:9

1 Answers

vikas askiitian expert
509 Points
10 years ago

let there is a particle at rest on the surface of earth in latitude @....  seudo force is acting on particle outwards &

real accleration due to gravity acts along the center of earth , then

Fc = seudo force = mW2r                    (r is distance of particle from center)

fg = force due to gravity = mg

net force towards center is F = (fg2 + Fc2+2fgFccos(180-@)1/2     (by vector law )

 

putting these values , F = m[(g2+(rW2)2 - 2grW2cos@)]1/2                  ...........1

 

          now  F = mgeff         .................2

from 1 & 2

     geff = [g2+(RW2)2 - 2grW2cos@]1/2                ..............3

now , W = 2pi/T          (T = 24hrs)

        W <<<<<<<<1  so we can neglect (rw2)2 , now

  geff = [g2 - 2grW2cos@]1/2

     r = Rcos@            (R is radius of earth)

geff = [ g2- 2gRW2cos2@]1/2

      = g[ 1 - 2RW2cos2@/g ]1/2 ,  this is similar to g[1-RW2cos2@/g]

geff = g - W2Rcos2@      ...................................4

this is the required result

 

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