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31 October, 07:23

Two masses are separated by a distance r. If this distance is doubled, is the force of interaction between the two masses doubled, halved, or changed by some other amount? explain

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  1. 31 October, 07:28
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    If the interaction is gravitational or electrical, it gets multiplied by (1/2-squared) or 1/4.
  2. 31 October, 07:42
    0
    Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

    This is mathematically represented as

    F = (G X m1 x m2) / r∧2

    where F is the force acting between the charged particles

    r is the distance between the two charges measured in m

    G is the gravitational constant which has a value of 6.674*10^-11 Nm^2 kg^-2

    m1 and m2 are the masses of the objects measured in Kg

    Now if the distance between the is doubled then r becomes 2r. Substituting this in the above formula we get the new Force as

    Force (new) = (G X m1 x m2) / (2r) ∧2

    Thus dividing Force (new) / Force we get

    Force (new) / Force = 1/4.

    Thus the gravitational force becomes 1/4th of the original value if the distance between the two masses are doubled.
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