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If the Earth has no rotational motion, the weight of a person on the equator is W . Determine the speed with which the earth would have to rotate about its axis so that the person at the equator will weigh 3 4 W . The radius of the Earth is 6400 km and g = 10 m s - 2

Options

  1. A0.63 × 10 - 3 r a d s - 1
  2. B0.28 × 10 - 3 rad s - 1
  3. C1.1 × 10 - 3 rad s - 1
  4. D0.83 × 10 - 3 rad s - 1

Correct answer

A. 0.63 × 10 - 3 r a d s - 1

Step-by-step solution

Due to the rotation of the earth, Changed gravitational acceleration, g ′ = g - ω 2 R cos 2 ⁡ θ At the equator, angle of inclination, θ = 0 3 g 4 = g - ω 2 R w 2 R = g 4 w = g 4 R = 10 4 × 6400 × 10 3 = 1 2 × 8 × 100 = 1 1600 = 1 16 × 10 - 2 = 0.6 × 10 - 3 rad s - 1 .

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