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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

A 1000 ext kg satellite is intended to orbit the earth at an altitude of 2000 ext km above the earth's surface. Determine its speed in the orbit. The mass of the earth is 6 imes 10²⁴ ext kg .

Options

  1. A7.92 ext km/s
  2. B8.25 ext km/s
  3. C6.90 ext km/s
  4. D5.45 ext km/s

Correct answer

C. 6.90 ext km/s

Step-by-step solution

The radius of the Earth is taken as R = 6400 km . The altitude of the satellite is h = 2000 km . The orbital radius of the satellite is r = R + h = 6400 + 2000 = 8400 km = 8.4 10^6 m . The orbital speed of a satellite is given by the formula: v = GM r Substituting the standard value of the gravitational constant G = 6.67 10⁻¹¹ N m ^2/ kg ^2 and the given mass of the Earth M = 6 10²⁴ kg : v = 6.67 10⁻¹¹ 6 10²⁴ 8.4 10^6 v = 40.02 10¹³ 8.4 10^6 v = 47.64 10^6 m/s v 6.90 10^3 m/s = 6.90 km/s

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