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Grade: 12
        
Variation of g with latitude 
I need the derivation for the formula
 
2 months ago

Answers : (2)

Saurabh Koranglekar
askIITians Faculty
2365 Points
29 days ago
Khimraj
2914 Points
							

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

29 days ago
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