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Shivam Bhagat Grade: 9
        pls derive G=g-w2.R.cosx

with every explanation plsssss!!!!!!
6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

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


 

6 years ago
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