What is an inverse-square relationship between force and distance? ( )a relation

Question

What is an inverse-square relationship between force and distance?

  ( )a relationship where increasing the distance by a factor increases the force by the square of the same factor

  (    )a relationship where the square of force is proportional to the square of the distance    

(    )a relationship where one value decreases in proportion to the square of the factor by which the other value decreases

  (     )a mathematical expression for the distance in terms of force instead of force in terms of distance, which is then squared

(     )a relationship where the increasing the distance by a factor decreases the force by dividing it by the square of that same factor

Explanation / Answer

Ans - a relationship where the increasing the distance by a factor decreases the force by dividing it by the square of that same factor

Take the case of gravitational force,
F = Gm1m2/r2,
Where G is the universal gravitational constant, m and m are the masses and r is the distance between them.
a) Increase r to 2r.
F2r = Gm1m2/(2r)2 = (1/4) Gm1m2/r2 = F/4.
b) Increase r to 3r.
F3r = Gm1m2/(3r)2 = (1/9) Gm1m2/r2 = F/9.
Similarly F4r gives F/16, F5r gives F/25 and so on. In all these cases, it can be seen that force decreases by a factor of dividing it by the square of the same factor. Electrostatics force also follows inverse square law.

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