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The distance between two masses M, and M₂ decreases by one third, the force between the bodies increases by what factor​

User Peque
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If the distance between two masses decreases by one third, the force between them will increase by a factor of 9.

How to calculate the force between two masses?

The gravitational force between two masses is given by Newton's law of universal gravitation.

F = Gm₁m₂ / r²

where;

  • G is the universal gravitation constant
  • m₁ is the mass of the first object
  • m₂ is the mass of the second object
  • r is the distance between the two objects

From the equation given above, we can see that force is inversely proportional to gravitational force.

F' = Gm₁m₂ / (¹/₃ r)²

F' = Gm₁m₂ / (¹/₉ r²)

F' = 9Gm₁m₂ / r²

F' = 9F

Thus, if the distance between two masses decreases by one third, the force between them will increase by a factor of 9.

User Pablo Blanco
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