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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 kinetic energy. The mass of the earth is 6 imes 10²⁴ ext kg .

Options

  1. A2.38 imes 10¹⁰ ext J
  2. B-2.38 imes 10¹⁰ ext J
  3. C1.19 imes 10¹⁰ ext J
  4. D4.76 imes 10¹⁰ ext J

Correct answer

A. 2.38 imes 10¹⁰ ext J

Step-by-step solution

Mass of the earth, M = 6 10²⁴ kg Radius of the earth, R = 6400 km = 6.4 10^6 m Altitude of the satellite, h = 2000 km = 2 10^6 m Orbital radius, r = R + h = 6.4 10^6 + 2 10^6 = 8.4 10^6 m Mass of the satellite, m = 1000 kg Gravitational constant, G = 6.67 10⁻¹¹ N m ^2/ kg ^2 The kinetic energy of a satellite in a circular orbit is given by: K = GMm 2r Substituting the values: K = 6.67 10⁻¹¹ 6 10²⁴ 1000 2 8.4 10^6 K = 40.02 10¹⁶ 16.8 10^6 K 2.38 10¹⁰ J

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