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

Answers : (2)

Saurabh Koranglekar
askIITians Faculty
3154 Points
4 months ago
Khimraj
3008 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

4 months ago
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