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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

In a nearly circular orbit of radius 3.84 10^5 km , the moon takes approximately 27.3 days to revolve around the earth. Determine the mass of the earth using these data.

Options

  1. A6.02 10²⁵ kg
  2. B6.02 10²³ kg
  3. C6.02 10²⁴ kg
  4. D1.52 10²⁴ kg

Correct answer

C. 6.02 10²⁴ kg

Step-by-step solution

The time period of a satellite revolving in a circular orbit of radius R around a central body of mass M is given by: T = 2 R^3 GM Squaring both sides and rearranging for M , we get: M = 4 ^2 R^3 GT^2 Given values are: R = 3.84 10^5 km = 3.84 10^8 m T = 27.3 days = 27.3 24 3600 s = 2.36 10^6 s G = 6.67 10⁻¹¹ N m ^2 kg ⁻² Substituting these values into the formula: M = 4 (3.14)^2 (3.84 10^8)^3 6.67 10⁻¹¹ (2.36 10^6)^2 M = 39.44 56.62 10²⁴ 6.67 10⁻¹¹ 5.57 10¹² M = 2233 10²⁴ 371.5 M 6.02 10²⁴ kg

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