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The effective value of the acceleration due to gravity changes with latitude owing to the rotation of the earth.
Referring to the figure , at a latitude θ (Point Q), the effective weight,
mg’ = mg − mω2 r cosθ …….(1)
where mω2 r is the “centrifugal force” and we take its component in the vertical direction and mg is the weight in the absence of rotation.
Now, r = radius of the circle of rotation of Q.
= QE = R cos θ (from ΔCQE),
Therefore, g’ = g − ω2 R cos2 θ
or, ….(2)
Now,
So, ω2 R/g ≅ 0.34%, which is indeed a very small effect
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