Question

1. which graph represents the relationship between the magnitude of the gravitational force, $f_g$, between two masses and the distance, $r$, between the centers of the masses?

(1) graph with $f_g$ vs $r$ as a straight line through origin
(2) graph with $f_g$ vs $r$ as a curve increasing with increasing slope
(3) graph with $f_g$ vs $r$ as a straight line decreasing to zero
(4) graph with $f_g$ vs $r$ as a curve decreasing with decreasing slope

Explanation:

Step1: Recall gravitational force formula

Newton's law of gravitation: $F_g = G\frac{m_1m_2}{r^2}$, where $G$, $m_1$, $m_2$ are constants.

Step2: Identify relationship type

$F_g$ is inversely proportional to $r^2$ (not linear inverse). This means as $r$ increases, $F_g$ decreases rapidly, forming a curve that approaches the axes but never touches them.

Step3: Match with graphs

Graph (1): Linear increase (wrong, $F_g$ doesn't increase with $r$).
Graph (2): Exponential increase (wrong).
Graph (3): Linear decrease (wrong, it's inverse square, not linear).
Graph (4): Inverse square curve (correct).

Answer:

(4)