Question

Which objects will likely have the smallest gravitational force between them?

A. Two tennis balls that are near each other

B. Two soccer balls that are near each other

C. Two tennis balls that are touching each other

D. Two soccer balls that are touching each other

Answer 1

B. Two soccer balls that are near each other

Step-by-step explanation:

You want to know the configuration of objects that has the least mutual gravitational attraction from ...

• tennis balls near each other
• soccer balls near each other
• tennis balls touching
• soccer balls touching

Gravity

Newton's law of universal gravitation says the force due to gravity between two objects is proportional to their masses and inversely proportional to the square of the distance between them.

This tells you that balls near each other will have less gravitational attraction than balls touching. This eliminates choices C and D.

Relative value

The meaning of the word "near" each other comes into play here. If we assume that the geometry of concern has the balls at the same distance relative to their diameter, then we can look a the mass a and diameter of a soccer ball and a tennis ball to determine which pair will have less gravitational attraction.

Here are the relevant specifications:

• soccer ball: 8.6-9" diameter, 400-450 g mass
• tennis ball: 2.575-2.7" diameter, 56-59.4 g mass

The fact that dimensions are mixed US and metric units is of no consequence. (The conversion factors will be the same in both cases.)

So, we can approximate the relative gravitational attraction with a "figure of merit" that is ...

fom = mass/diameter²

The attached calculator shows this figure of merit for the two ball types. The lesser value corresponds to the lesser force of gravity between soccer balls.

fom (soccer ball) ≈ 4.9

fom (tennis ball) ≈ 7.7

Two soccer balls near each other will have the smallest gravitational force.

Answer 2

Answer: A. Two tennis balls that are near each other

Explanation: The gravitational force between two objects depends on their masses and the distance between them. According to Newton's law of universal gravitation, the force of gravity is directly proportional to the product of the masses and inversely proportional to the square of the distance between the objects.

In this scenario and given the information provided, the tennis balls are near each other but not touching, the distance between them is small. Furthermore, tennis balls have relatively low mass and are smaller compared to soccer balls. So, the gravitational force between them will be relatively small.