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NTA Abhyas JEE Main2020PhysicsGravitationPractice

How many time faster than the present speed would the earth have to rotate about its axis so that the apparent weight of the bodies on the equator becomes zero? (The radius of the earth R = 6 .4 × 10 6 m )

Options

  1. A5   times
  2. B9   times
  3. C13   times
  4. D17   times

Correct answer

D. 17   times

Step-by-step solution

Let ω 0 be the new angular velocity. At the equator g E = g - R ω 2 The weight m g E should be zero. g E = 0 ∴ R ω 0 2 = g or ω 0 = g R ∴ ω 0 = 9.8 6.4 × 1 0 6 = 1.24 × 1 0 - 3 r a d s The present angular velocity of the earth is ω = 2 π T = 2 × 3.14 24 × 60 × 60 ∴ ω = 3.14 × 1 0 - 2 12 × 36 = 7.27 × 1 0 - 5 ∴ ω 0 ω = 1.24 × 1 0 - 3 7.27 × 1 0 - 5 = 17 ∴ ω 0 = 17 ω It should rotate faster by 17 times the present value.

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