Question

The Earth is rotating with angular velocity o about its own axis. R is the radius of the Earth.
If Ro? = 0.03386m/s?, calculate the weight of a body of mass 100 gram at latitude 25º.
(g = 9.8 m/s?)
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Answer 1

Answer:

The weight of the body at latitude 25° is 0.9772 N

Explanation:

If θ is the latitude of a place, R is the radius of the Earth, ω is the angular velocity of the earth then the apparent weight of an object of mass m will be

W' = mg - mRω²cos²θ

Given

Rω² = 0.03386 m/s²

m = 100 gm = 0.1 kg

θ = 25°

Therefore the weight of the body

W' = 0.1 × 9.8 - 0.1 × 0.03386 cos²25°

    = 0.1(9.8 - 0.03386 × 0.8234)

    = 0.1 × (9.8 - 0.0278)

    = 0.9772 N