Question

Which of the following sentences is true about the relationship between distance and gravitational force? [mark all correct answers] a. Smaller distance results in greater force. b. Smaller mass results in greater force. c. Greater distance results in no force. d. Greater mass results in greater force.

Answer 1

For the gravitational attraction between two point masses:

• Smaller distance results in greater force, and
• Greater mass results in greater force.

Step-by-step explanation:

Between two point masses
`M` and
`m`, the magnitude of gravitational attraction is:

`\displaystyle (G\, M\, m)/(r^(2))`,

Where:

• 
  `G` is the gravitational constant, and
• 
  `r` is the distance between the two objects.

Note that the distance
`r` between the two objects is in the denominator of the expression for the force. If the value of distance
`r\!` becomes smaller, the value of the denominator will become smaller, and the value of the fraction will increase. In other words, reducing distance between the two point masses will increase the magnitude of gravitational attraction between them.

The mass of the two objects are in the numerator of the expression for the force. Assume that one of the two point masses and the distance between the two stay the same. If the mass of the other object increases, the numerator of this fraction will increase, and the value of the fraction will also increase.

Hence, increasing the mass of one of the two objects will increase the magnitude of the gravitational attraction between the two objects.