Question

Consider Newton's Law of Universal Gravitation: FG= G (m1 m2)/d2 .

Which statement is true of the relationship between force, mass, and distance?

A
Mass and Distance are directly proportional to the Force of Gravity. If either increases, then the Force of Gravity increases.

B
Mass and Distance are indirectly (or inversely) proportional to the Force of Gravity. If either increases, then the Force of Gravity decreases.

C
Mass is directly proportional to the Force of Gravity. If Mass increases, then the Force of Gravity increases; however, Distance is indirectly (or inversely) proportional to the Force of Gravity. If Distance increases, then the Force of Gravity decreases.

D
Mass is indirectly (or inversely) proportional to the Force of Gravity. If Mass increases, then the Force of Gravity decreases; however, Distance is directly proportional to the Force of Gravity. If Distance increases, then the Force of Gravity increases.

Answer 1

C. Mass is directly proportional to the Force of Gravity. If Mass increases, then the Force of Gravity increases; however, Distance is indirectly (or inversely) proportional to the Force of Gravity. If Distance increases, then the Force of Gravity decreases.

Step-by-step explanation:

According to the Newton's law of gravitation which states that, the force between between masses is directly proportional to the product of the masses and inversely proportional to the square of the distance between them.

Mathematically,

F ∝ Mm and F ∝ 1/d²

Where M and m are the masses

d is the distance between the masses

F = GMm and F = 1/d²

Since gravitational force is directly proportional to the masses, this means an INCREASE in the masses leads to INCREASE in gravitational force between them and vice versa.

Similarly, since the gravitational force is inversely proportional to the distance between them, this means that INCREASE in the distance leads to DECREASE in the gravitational force between them.

Answer 2

C

Mass is directly proportional to the Force of Gravity. If Mass increases, then the Force of Gravity increases; however, Distance is indirectly (or inversely) proportional to the Force of Gravity. If Distance increases, then the Force of Gravity decreases.

Step-by-step explanation:

The formula for the force of gravity between two objects is

`F=G(m_1 m_2)/(d^2)`

where

G is the gravitational constant

m1, m2 are the masses of the two objects

d is the separation between the two objects

We notice the following:

- F is directly proportional to the masses,
`F\propto m_1, m_2`. This means that if one of the masses increases, then the force between them, F, increases in a proportional way

- F is inversely proportional to the square of the distance,
`F\propto (1)/(d^2)`. This means that if the distance between the two objects is increased, the force between them will decrease, and vice-versa.

So, the correct answer is

C

Mass is directly proportional to the Force of Gravity. If Mass increases, then the Force of Gravity increases; however, Distance is indirectly (or inversely) proportional to the Force of Gravity. If Distance increases, then the Force of Gravity decreases.