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Question

How does the gravitational force between two given objects change when the distance between them is reduced to one-half of its original value?


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Solution

  1. Let the masses of two given objects be M and m, and the distance between them be R.
  2. Then, the magnitude of the gravitational force of attraction (F) between them is shown as F=GMmR2.
  3. Let the value of the distance between them, after it gets halved be R2.
  4. The magnitude of the gravitational force of attraction (F') after the distance is one-halved, is given by F'=GMm(R2)2=GMmR24=4GMmR2=4F
  5. Hence, the gravitational force between the two given objects becomes four times the original value when the distance between them is reduced to one-half of its original value.

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