Newton Law Gravitation - Multiple choice question?

[jsmith613]

Newton Law Gravitation - Multiple choice question??

Homework Statement

Newton’s law of gravitation can be applied to the Earth-Moon system. Which of the
following statements is not correct?

A The value of G at the surface of the Moon is the same as that at the surface
of the Earth.
B The gravitational force between the Earth and the Moon is proportional to the
square of the separation of the Earth and the Moon.
C The gravitational force between the Earth and the Moon is proportional to the
mass of the Moon.
D The orbital time of the Moon about the Earth is independent of the mass of
the Moon

Homework Equations

The Attempt at a Solution

Lets go through all the options:

A: G is constant so option A is is not the answer
B: F = GMm/r² so option B is is not the answer
C: using the same equation as above, option C is is not the answer
D: T = ^4∏2r3 /_GM where M = mass of Earth so option D is not the answer

The answer turns out to be B. Why?

 

[jsmith613]

oh of course its an inverse relationship
SMACK!

 

[Whovian]

B. Note that since [itex]\displaystyle{g=\dfrac{G\cdot m\cdot M}{r^2}}[/itex], the force is proportional to the inverse of the square of the radius, or inversely proportional to the square of the radius.

EDIT: Oops, a bit late. Never mind.

 

[jsmith613]

B. Note that since [itex]\displaystyle{g=\dfrac{G\cdot m\cdot M}{r^2}}[/itex], the force is proportional to the inverse of the square of the radius, or inversely proportional to the square of the radius.

EDIT: Oops, a bit late. Never mind.

cheers anyway :)

 

[asteriatic]

Because the gravitational force between the Earth and the Moon is actually proportional to the product of their masses, not the square of their separation. The correct answer would be "The gravitational force between the Earth and the Moon is proportional to the product of their masses."