Question

You hold a tennis ball above your head, then open your hand and release the ball, which begins to fall. At this instant (ball starting to fall, no longer in contact with your hand), what can you conclude about the relative magnitudes of the force on the ball by the Earth and the force on the Earth by the ball? Explain.

Short answer

The magnitudes of the force on the ball by the Earth and the force on the Earth by the ball are the same.

Step-by-step solution

Gravitational Force 

It is responsible for the attraction between the object that mass. And it depends on the mass and radius of the object.

Force on the Earth by the ball

Force on the Earth by the ball can be expressed as

$F_{EB}=\frac{G{M}_E{M}_B}{R}$

Where $G$= universal gravitational constant,

$M_E$= mass of earth,

$M_B$= mass of the ball,

$R$ = is radius

The direction of the force is from the ball pointing to the center of the Earth.

Force on the ball by the Earth

Force on the Earth by the ball can be expressed as

$$\begin{gathered} \left|F_{BE}\right|=\left|-F_{EB}\right| \\ {\stackrel{\rightharpoonup }{F}}_{EB}=\frac{G{M}_E{M}_B}{R} \end{gathered}$$

The negative sign indicated that the force on the Earth by the ball was in the opposite direction.

The direction of force is from the center of Earth pointing to the ball.

Thus, it is concluded that the magnitude of the force on the ball by the Earth and the force on the Earth by the ball are the same.