Chapter 4, Problem 1QP

To determine

The quantity that is proportional to force in Newton’s Universal law of gravitation.

Answer to Problem 1QP

Option (a) proportional to both masses.

Explanation of Solution

Write the formula for Newton’s Universal Law of Gravity

    $F_{grav}=G\times \frac{M_1{M}_2}{r^2}$

Here, $F_{grav}$ is the force due to gravity, $G$ is the Universal gravitational constant, $M_1\text{ and }{M}_2$ are the masses and $r$ is the distance between the masses.

Therefore, according to Newton’s Universal law of gravitation, force is directly proportional to the masses and inversely proportional to the square of the distance between them.

Conclusion:

Force is proportional to both masses. Thus, option (A) is correct.

Force is not proportional to the radius. Thus, option (B) is incorrect.

Force is not proportional to the radius squared. Thus, option (C) is incorrect.

Force is not inversely proportional to the orbiting mass. Thus, option (D) is incorrect.