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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

Determine the rate at which the earth must rotate so that the apparent g at the equator becomes zero. What will be the length of the day in this situation?

Options

  1. A1.237 10⁻³ rad/s , 1.41 h
  2. B2.474 10⁻³ rad/s , 0.70 h
  3. C0.618 10⁻³ rad/s , 2.82 h
  4. D1.237 10⁻³ rad/s , 24 h

Correct answer

A. 1.237 10⁻³ rad/s , 1.41 h

Step-by-step solution

The apparent acceleration due to gravity at the equator is given by g' = g - R ^2 For the apparent gravity to be zero, g' = 0 g - R ^2 = 0 = g R Substituting g = 9.8 m/s ^2 and R = 6.4 10^6 m = 9.8 6.4 10^6 = 1.237 10⁻³ rad/s The length of the day in this situation will be T = 2 T = 2 3.14 1.237 10⁻³ = 5077 s Converting into hours T = 5077 3600 h = 1.41 h

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