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How will the value of the acceleration d...

How will the value of the acceleration due to gravity be affected if

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Due to the rotation of the earth, the outward centrifugal force acting on bodies on bodies on the earth.s surface and directed away from the centre of the earth decreases the weight of these bodies slightly. Hence, there is a small apparent change in g.
Apparent weight `=mg^. =mg=momega^2R cos^2theta,g^.=` effective acceleration due to gravity ,g=actual value of the acceleration due to gravity, `omega`= angular velocity of the earth, R= radius of earth, `theta`=latitude of the place.
`therefore g^.=g-omega^2R cos^2theta`.
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Knowledge Check

  • If the earth is assumed to be a sphere of radius R, the height above the surface of the earth where the value of the acceleration due to gravity will be half its value on the earth's surface is

    A
    `h=R/2`
    B
    `h=R/sqrt(2)`
    C
    `h=(sqrt(2)+1)R`
    D
    `h=(sqrt(2)-1)R`

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