What happens to the gravitational field strength's magnitude if

[chaishreen]

Homework Statement

What happens to the gravitational field strength's magnitude if
a) r decreases by a factor of 4?
b) r increases by factor of 2

Homework Equations

i'm not sure which equation they are referring to? it may be g ∝ 1/r^2

The Attempt at a Solution

I tried to do this:
1/ (r-4)^2 and i got 1/(r^2 - 8r + 16)
the answer at the back of the book for a) says gravitational field strength's magnitude is supposed to become 16 times greater and for b) it's supposed to become 1/4 as great
please help

 

[PeterO]

Homework Statement

What happens to the gravitational field strength's magnitude if
a) r decreases by a factor of 4?
b) r increases by factor of 2

Homework Equations

i'm not sure which equation they are referring to? it may be g ∝ 1/r^2

The Attempt at a Solution

I tried to do this:
1/ (r-4)^2 and i got 1/(r^2 - 8r + 16)
the answer at the back of the book for a) says gravitational field strength's magnitude is supposed to become 16 times greater and for b) it's supposed to become 1/4 as great
please help

The radius has not decreased by 4, but by a factor of 4.

So r → r/4 (rather than r → r-4)

 

[chaishreen]

hey thanks, but is it g ∝ 1/(r/4)^2?

 

[CAB12]

Fg=Gmm/r^2 so if you bring the masses 4 times closer and Gmm remain the same, then Fg' = Gmm/(r/4)^2. It follows that Fg'=Gmm/(r^2/4^2) which is Gmm/r^2/16, thus 16 (Gmm/r^2). Since Gmm/r^2is the original force, the new one is 16 times greater.

Likewise you can show that increasing r to 2r will make (2r)^2 = 4r^2, so the force will be 4 times smaller.

 

[PeterO]

hey thanks, but is it g ∝ 1/(r/4)^2?

Expand that expression and what do you get? Compare it to the original 1/r²

 

[PeterO]

Homework Statement

What happens to the gravitational field strength's magnitude if
a) r decreases by a factor of 4?
b) r increases by factor of 2

Homework Equations

i'm not sure which equation they are referring to? it may be g ∝ 1/r^2

The Attempt at a Solution

I tried to do this:
1/ (r-4)^2 and i got 1/(r^2 - 8r + 16)
the answer at the back of the book for a) says gravitational field strength's magnitude is supposed to become 16 times greater and for b) it's supposed to become 1/4 as great
please help

Also a simple approach is: this is an example if an "inverse square law" [some others are intensity of light, intensity of sound, electrical attraction between charges ...]

The inverse part tells you the change is opposite: reduce the separation - increase the force.
The square part tells you the size of change. change "r" by a factor of 4 → a "g" change of 4² (which is 16).