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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

Determine the acceleration due to gravity inside a mine at a depth of 640 m , assuming the surface value is 9.800 m/s ^2 . The radius of the earth is 6400 km .

Options

  1. A9.798 m/s ^2
  2. B9.799 m/s ^2
  3. C9.801 m/s ^2
  4. D8.820 m/s ^2

Correct answer

B. 9.799 m/s ^2

Step-by-step solution

The acceleration due to gravity at a depth d is given by the formula: g_d = g (1 - d R ) Substituting g = 9.800 m/s ^2 , d = 640 m = 0.64 km , and R = 6400 km : g_d = 9.800 (1 - 0.64 6400 ) g_d = 9.800 (1 - 1 10000 ) g_d = 9.800 (1 - 0.0001) g_d = 9.800 0.9999 g_d = 9.79902 m/s ^2 Rounding to three decimal places, the value is 9.799 m/s ^2 .

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