Question

The force of gravity cannot act at a distance. State true or false
A) True
B) False

Answer 1

Recall Newton’s law of gravitation i.e. the gravitational force of attraction between Earth and a body is given by:
$F = G\dfrac{{Mm}}{{{r^2}}}$
Where $M$ is the mass of the earth and $m$ is the mass of the body, $G$ is the universal gravitational constant and $r$ is the distance between the centers of the earth and the body.
From this equation, we can determine the various factors on which the force of gravity depends.

Complete step by step answer:
From Newton’s Law of gravitation between the earth and a body, the force of gravity is given by:
$F = G\dfrac{{Mm}}{{{r^2}}}$
Where $M$ is the mass of the earth and $m$is the mass of the body, $G$ is the universal gravitational constant and $r$ is the distance between the centers of the earth and the body.
Since here $G$, $M$, and $m$ are constants. Therefore,
$F \propto \dfrac{1}{{{r^2}}}$
From above it is clear that the force of gravity between the earth and a body is inversely proportional to the distance between the centers of the earth and body.

Hence this statement is false that “The force of gravity cannot act at a distance”. Therefore option B is the correct answer.

Note:
Keep in mind that there is a difference between ‘$g$’ and ‘$G$’. The ‘$g$’ is the acceleration due to gravity whereas the ‘G’ is the universal gravitation constant. The value of ‘$G$’ is $6.67 \times {10^{ - 11}}N{m^2}/k{g^2}$ and this remains constant throughout the universe whereas the value of ‘$g$’ is $9.81m/{s^2}$ on the surface of the earth and it will keep changing as we move up or down from the surface of the earth.