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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

Determine the acceleration due to gravity of the moon at a location 1000 km above its surface. The moon's mass is 7.4 10²² kg and its radius is 1740 km .

Options

  1. A4.94 m/s ^2
  2. B0.65 m/s ^2
  3. C1.63 m/s ^2
  4. D1.04 m/s ^2

Correct answer

B. 0.65 m/s ^2

Step-by-step solution

The acceleration due to gravity at a height h above the surface of the moon is given by: g' = GM (R+h)^2 Given: Mass of the moon, M = 7.4 10²² kg Radius of the moon, R = 1740 km = 1.74 10^6 m Height above the surface, h = 1000 km = 1.0 10^6 m Distance from the center, r = R + h = 2740 km = 2.74 10^6 m Gravitational constant, G 6.67 10⁻¹¹ N m ^2/ kg ^2 Substituting the values: g' = 6.67 10⁻¹¹ 7.4 10²² (2.74 10^6)^2 g' = 49.358 10¹¹ 7.5076 10¹² g' 0.65 m/s ^2

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