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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

The acceleration of the moon with respect to the earth is 0.0027 m/s ^2 , whereas the acceleration of an apple falling on the earth's surface is approximately 10 m/s ^2 . Taking the radius of the moon to be one fourth of the earth's radius, suppose the moon is momentarily stopped and then released so that it falls towards the earth. The acceleration of the moon just before it strikes the earth is

Options

  1. A10 m/s ^2
  2. B0.0027 m/s ^2
  3. C6.4 m/s ^2
  4. D5.0 m/s ^2

Correct answer

C. 6.4 m/s ^2

Step-by-step solution

The acceleration due to gravity on the surface of the earth is given by: g = GM_e R_e^2 = 10 m/s ^2 When the moon is just about to strike the earth, the distance between their centers is equal to the sum of their radii: r = R_e + R_m Given that the radius of the moon is one fourth of the earth's radius ( R_m = R_e 4 ): r = R_e + R_e 4 = 5R_e 4 The acceleration of the moon at this distance is: a = GM_e r^2 = GM_e ( 5R_e 4 )^2 = 16 25 GM_e R_e^2 Substituting the value of g : a = 16 25 10 = 6.4 m/s ^2 Answer: 6.4 m/s

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