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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 the potential energy of the earth-satellite system. The mass of the earth is 6 imes 10²⁴ ext kg .

Options

  1. A-4.76 imes 10¹⁰ ext J
  2. B2.38 imes 10¹⁰ ext J
  3. C-2.38 imes 10¹⁰ ext J
  4. D4.76 imes 10¹⁰ ext J

Correct answer

A. -4.76 imes 10¹⁰ ext J

Step-by-step solution

The potential energy of the earth-satellite system is given by: U = - GMm r where r is the distance of the satellite from the center of the earth. Given: m = 1000 kg M = 6 10²⁴ kg R = 6400 km = 6.4 10^6 m h = 2000 km = 2 10^6 m Distance from the center of the earth, r = R + h = 8.4 10^6 m Substituting the values: U = - 6.67 10⁻¹¹ 6 10²⁴ 1000 8.4 10^6 U = - 40.02 10¹⁶ 8.4 10^6 U -4.76 10¹⁰ J

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